Traditionally, physics has been considered the most difficult science, which should only be attempted by mature students with a strong mathematicalbackground. There is some truth to this- being comfortable with advanced math can certainly open up some areas of physics and there are topics in a solid, college-preparatory physics class that require some pretty serious number-crunching. However, there is another side to this story and a growing feeling among educators (myself included) that even elementary school students can and should study physics.
One of the strongest arguments for introducing physics at a young age is that it is the most "basic" of the sciences. In other words, it's really not possible to have a good understanding ofphotosynthesis if you don't know anything about light. Learning about light is, of course, a branch of physics.
There's currently a "physics first" movement that is trying to upend the traditional order of high school science classes so that the sequence becomes physics in freshman year, then chemistry, and finally biology. In this model, physics is taught as a more conceptual and less calculation-based subject because younger students do not have the mathematical knowledge of older ones.
Physics first could be the best thing that ever happened to physics education, if it is done correctly. Beyond the obvious perk for physics-enthusiasts everywhere that physics would studied by far more people than ever before, it could potentially be taught much more effectively. One of the flaws in traditional physics education is that it assumes that students will learn the concepts that the mathematics illustrate by applying the math to problems. Unfortunately, this doesn't work well most of the time. Most people need to approach physics from a conceptual point of view before they can understand the mathematics in a meaningful way. This is true even for smart, mathematically inclined people, and it is at least part of the reason that so many people learn so little in high school physics classes. In essence, the goal of physics first education is to help all students achieve a solid qualitative understanding of the physical world. Interested students can then refine that pre-existing qualitative knowledge into a quantitative understanding in a later, more advanced class.
The philosophy behind physics first doesn't have to be restricted to educating high school freshmen. It can effectively be applied to much younger children as well. For example, I teach science to a group of nine and ten year old homeschoolers, and we have done quite a bit of physics, with very little math beyond basic arithmetic. For example, last year we explored levers and turning effect. This year we will be looking into pulleys and simple circuits. I don't shy away from using age-appropriate math, including simple formulas, but neither do I emphasize formulas over a verbal understanding of events. These kids are hardly advanced physics students, but they have achieved significant understanding while retaining a strong interest in learning more.
Critics of a conceptual approach to physics education worry that it is merely a way to lower standards. I share their desire for the highest standards possible, and I acknowledge that a poorly executed conceptual physics program could lack rigor. As always, details matter. A good conceptual physics program should involve hands-on (and "brain-on") experiments, extensive writing, and some math. It should not be easy. On the other hand, it shouldn't leave conscientious, hard working students feeling like they are studying an impossible subject- and traditional physics education leaves far too many students with that feeling.
Tuesday, January 5, 2010
Conceptual Physics
Sunday, January 3, 2010
A History of Quantum Mechanics
It is hard to realise that the electron was only discovered a little over 100 years ago in 1897. That it was not expected is illustrated by a remark made by J J Thomson, the discoverer of the electron. He said I was told long afterwards by a distinguished physicist who had been present at my lecture that he thought I had been pulling their leg. The neutron was not discovered until 1932 so it is against this background that we trace the beginnings of quantum theory back to 1859. In 1859 Gustav Kirchhoff proved a theorem about blackbody radiation. A blackbody is an object that absorbs all the energy that falls upon it and, because it reflects no light, it would appear black to an observer. A blackbody is also a perfect emitter and Kirchhoff proved that the energy emitted E depends only on the temperature T and the frequency v of the emitted energy, i.e. E = J(T,v). He challenged physicists to find the function J. In 1879 Josef Stefan proposed, on experimental grounds, that the total energy emitted by a hot body was proportional to the fourth power of the temperature. In the generality stated by Stefan this is false. The same conclusion was reached in 1884 by Ludwig Boltzmann for blackbody radiation, this time from theoretical considerations using thermodynamics and Maxwell's electromagnetic theory. The result, now known as the Stefan-Boltzmann law, does not fully answer Kirchhoff's challenge since it does not answer the question for specific wavelengths. In 1896 Wilhelm Wien proposed a solution to the Kirchhoff challenge. However although his solution matches experimental observations closely for small values of the wavelength, it was shown to break down in the far infrared by Rubens and Kurlbaum. Kirchhoff, who had been at Heidelberg, moved to Berlin. Boltzmann was offered his chair in Heidelberg but turned it down. The chair was then offered to Hertz who also declined the offer, so it was offered again, this time to Planck and he accepted. Rubens visited Planck in October 1900 and explained his results to him. Within a few hours of Rubens leaving Planck's house Planck had guessed the correct formula for Kirchhoff's J function. This guess fitted experimental evidence at all wavelengths very well but Planck was not satisfied with this and tried to give a theoretical derivation of the formula. To do this he made the unprecedented step of assuming that the total energy is made up of indistinguishable energy elements - quanta of energy. He wrote Experience will prove whether this hypothesis is realised in nature Planck himself gave credit to Boltzmann for his statistical method but Planck's approach was fundamentally different. However theory had now deviated from experiment and was based on a hypothesis with no experimental basis. Planck won the 1918 Nobel Prize for Physics for this work. In 1901 Ricci and Levi-Civita published Absolute differential calculus. It had been Christoffel's discovery of 'covariant differentiation' in 1869 which let Ricciextend the theory of tensor analysis to Riemannian space of n dimensions. The Ricci and Levi-Civita definitions were thought to give the most general formulation of a tensor. This work was not done with quantum theory in mind but, as so often happens, the mathematics necessary to embody a physical theory had appeared at precisely the right moment. In 1905 Einstein examined the photoelectric effect. The photoelectric effect is the release of electrons from certain metals or semiconductors by the action of light. The electromagnetic theory of light gives results at odds with experimental evidence. Einstein proposed a quantum theory of light to solve the difficulty and then he realised that Planck's theory made implicit use of the light quantum hypothesis. By 1906 Einstein had correctly guessed that energy changes occur in a quantum material oscillator in changes in jumps which are multiples of In 1913 Niels Bohr wrote a revolutionary paper on the hydrogen atom. He discovered the major laws of the spectral lines. This work earned Bohr the 1922 Nobel Prize for Physics. Arthur Compton derived relativistic kinematics for the scattering of a photon (a light quantum) off an electron at rest in 1923. However there were concepts in the new quantum theory which gave major worries to many leading physicists. Einstein, in particular, worried about the element of 'chance' which had entered physics. In fact Rutherford had introduced spontaneous effect when discussing radio-active decay in 1900. In 1924 Einstein wrote:- There are therefore now two theories of light, both indispensable, and - as one must admit today despite twenty years of tremendous effort on the part of theoretical physicists - without any logical connection. In the same year, 1924, Bohr, Kramers and Slater made important theoretical proposals regarding the interaction of light and matter which rejected the photon. Although the proposals were the wrong way forward they stimulated important experimental work. Bohr addressed certain paradoxes in his work. (i) How can energy be conserved when some energy changes are continuous and some are discontinuous, i.e. change by quantum amounts. Einstein had been puzzled by paradox (ii) and Pauli quickly told Bohr that he did not believe his theory. Further experimental work soon ended any resistance to belief in the electron. Other ways had to be found to resolve the paradoxes. Up to this stage quantum theory was set up in Euclidean space and used Cartesian tensors of linear and angular momentum. However quantum theory was about to enter a new era. The year 1924 saw the publication of another fundamental paper. It was written by Satyendra Nath Bose and rejected by a referee for publication. Bose then sent the manuscript to Einstein who immediately saw the importance of Bose's work and arranged for its publication. Bose proposed different states for the photon. He also proposed that there is no conservation of the number of photons. Instead of statistical independence of particles, Bose put particles into cells and talked about statistical independence of cells. Time has shown that Bose was right on all these points. Work was going on at almost the same time as Bose's which was also of fundamental importance. The doctoral thesis of Louis de Broglie was presented which extended the particle-wave duality for light to all particles, in particular to electrons. Schrödinger in 1926 published a paper giving his equation for the hydrogen atom and heralded the birth of wave mechanics. Schrödinger introduced operators associated with each dynamical variable. The year 1926 saw the complete solution of the derivation of Planck's law after 26 years. It was solved by Dirac. Also in 1926 Born abandoned the causality of traditional physics. Speaking of collisions Born wrote One does not get an answer to the question, What is the state after collision? but only to the question, How probable is a given effect of the collision? From the standpoint of our quantum mechanics, there is no quantity which causally fixes the effect of a collision in an individual event. Heisenberg wrote his first paper on quantum mechanics in 1925 and 2 years later stated his uncertainty principle. It states that the process of measuring the position xof a particle disturbs the particle's momentum p, so that Dx Dp ≥ where Dx is the uncertainty of the position and Dp is the uncertainty of the momentum. Here h is Planck's constant and the nonvalidity of rigorous causality is necessary and not just consistently possible. Heisenberg's work used matrix methods made possible by the work of Cayley on matrices 50 years earlier. In fact 'rival' matrix mechanics deriving fromHeisenberg's work and wave mechanics resulting from Schrödinger's work now entered the arena. These were not properly shown to be equivalent until the necessary mathematics was developed by Riesz about 25 years later. Also in 1927 Bohr stated that space-time coordinates and causality are complementary. Pauli realised that spin, one of the states proposed by Bose, corresponded to a new kind of tensor, one not covered by the Ricci and Levi-Civita work of 1901. However the mathematics of this had been anticipated by Eli Cartan who introduced a 'spinor' as part of a much more general investigation in 1913. Dirac, in 1928, gave the first solution of the problem of expressing quantum theory in a form which was invariant under the Lorentz group of transformations of special relativity. He expressed d'Alembert's wave equation in terms of operator algebra. The uncertainty principle was not accepted by everyone. Its most outspoken opponent was Einstein. He devised a challenge to Niels Bohr which he made at a conference which they both attended in 1930. Einstein suggested a box filled with radiation with a clock fitted in one side. The clock is designed to open a shutter and allow one photon to escape. Weigh the box again some time later and the photon energy and its time of escape can both be measured with arbitrary accuracy. Of course this is not meant to be an actual experiment, only a 'thought experiment'. Niels Bohr is reported to have spent an unhappy evening, and Einstein a happy one, after this challenge by Einstein to the uncertainty principle. However Niels Bohrhad the final triumph, for the next day he had the solution. The mass is measured by hanging a compensation weight under the box. This is turn imparts a momentum to the box and there is an error in measuring the position. Time, according to relativity, is not absolute and the error in the position of the box translates into an error in measuring the time. Although Einstein was never happy with the uncertainty principle, he was forced, rather grudgingly, to accept it after Bohr's explanation. In 1932 von Neumann put quantum theory on a firm theoretical basis. Some of the earlier work had lacked mathematical rigour, but von Neumann put the whole theory into the setting of operator algebra.
(ii) How does the electron know when to emit radiation.
Eistein on the Photoelectric Effect
Light and other electromagnetic radiation, such as radio waves, are obviously waves—or so everyone thought. Maxwell and Lorentz had firmly established the wave nature of electromagnetic radiation in electromagnetic theory. Numerous experiments on the interference, diffraction, and scattering of light had confirmed it. We can well appreciate the shock and disbelief when Einstein argued in 1905 that under certain circumstances light behaves not as continuous waves but as discontinuous, individual particles. These particles, or "light quanta," each carried a "quantum," or fixed amount, of energy, much as automobiles produced by an assembly plant arrive only as individual, identical cars—never as fractions of a car. The total energy of the light beam (or the total output of an assembly plant) is the sum total of the individual energies of these discrete "light quanta" (or automobiles), what are called today "photons." Theories of matter and electromagnetic radiation in which the total energy is treated as "quantized" are known as quantum theories. Although Einstein was not the first to break the energy of light into packets, he was the first to take this seriously and to realize the full implications of doing so. Like the special theory of relativity, Einstein's quantum hypothesis arose from an experimental puzzle and an asymmetry or duality in physical theories. The duality consisted of the well-known distinction between material atoms and continuous ether, or, as Einstein wrote in the opening sentence of his light quantum paper, "between the theoretical conceptions that physicists have formed about gases and other ponderable bodies and the Maxwell theory of electromagnetic processes in so-called empty space." As noted earlier, Boltzmann and others conceived of gases as consisting of myriads of individual atoms, while Maxwell and Lorentz envisioned electromagnetic processes as consisting of continuous waves. Einstein sought a unification of these two viewpoints by removing the asymmetry in favor of a discontinuous, "atomic," or quantum, theory of light. Resolution of an experimental puzzle encouraged this approach. The puzzle concerned so-called blackbody radiation, that is, the electro-magnetic radiation given off by a hot, glowing coal in a fireplace, or the radiation emerging from a small hole in a perfectly black box containing electromagnetic radiation at a high temperature. Scientists at the German bureau of standards in Berlin, who were interested in setting standards for the emerging electric lighting industry in Germany, had measured the distribution of the total electromagnetic energy in a black box—which would also apply to a glowing light bulb—among the different wavelengths of the light. But no one until Max Planck, at the turn of the century, was able to give a single mathematical formula for the observed distribution of the energy among the emitted wavelengths. Starting with the Maxwell-Lorentz theory of radiation and some natural assumptions about energy, Planck hoped to derive this formula from the second law of thermodynamics. Planck failed to attain the observed formula on these assumptions. Even Lorentz had to admit that his own electron theory could not account for blackbody radiation. Only by reluctantly introducing a radical new assumption into his mathematics could Planck attain the correct formula. The assumption was that the energy of the radiation does not act continuously, as one would expect for waves, but exerts itself in equal discontinuous parcels, or "quanta," of energy. In essence Planck had discovered the quantum structure of electromagnetic radiation. But Planck himself did not see it that way; he saw the new assumption merely as a mathematical trick to obtain the right answer. Its significance remained for him a mystery. Thomas Kuhn has argued that it is not to Planck in 1900 but to Einstein in 1905 that we owe the origins of quantum theory. Encouraged by his brief but successful application of statistical mechanics to radiation in 1904, in 1905 Einstein attempted to resolve the duality of atoms and waves by demonstrating that part of Planck's formula can arise only from the hypothesis that electromagnetic radiation behaves as if it actually consists of individual "quanta" of energy. The continuous waves of Maxwell's equations, which had been confirmed experimentally, could be considered only averages over myriads of tiny light quanta, essentially "atoms" of light. With his light quantum hypothesis Einstein could not only derive part of Planck's formula but also account directly for certain hitherto inexplicable phenomena. Foremost among them was the photoelectric effect: the ejection of electrons from a metal when irradiated by light. The wave theory of light could not yield a satisfactory account of this, since the energy of a wave is spread over its entire surface. Light quanta, on the other hand, acting like little particles, could easily eject electrons, since the electron absorbs the entire quantum of energy on impact. At first Einstein believed that the light-quantum hypothesis was merely "heuristic": light behaved only as if it consisted of discontinuous quanta. But in a brilliant series of subsequent papers in 1906 and 1907, Einstein used his statistical mechanics to demonstrate that when light interacts with matter, Planck's entire formula can arise only from the existence of light quanta—not from waves. Einstein considered that light quanta, together with the equivalence of mass and energy, might result in a reduction of electrodynamics to an atom-based mechanics. But in 1907 he Here he made use of another galling experimental problem. Experimentalists had found that when solid bodies were cooled, the amount of heat they lost failed to fit a simple formula that followed from Newtonian mechanics. Einstein showed that the experiments could be explained only on the assumption that the oscillating atoms of the solid lattice can have only certain, specific energies, and nothing in between. In other words, even the motions of atoms—which are continuous in Newtonian mechanics—exhibit a quantum structure. Mechanics and electrodynamics both required radical revision, Einstein now concluded: neither could yet account for the existence of electrons or energy quanta.
discovered that atoms in matter are also subject to a quantum effect.
Modern Metaphysical Cosmology
You may or may not be aware that cosmology is not a basic term. There are many types of cosmology, and each one is looked at in a different way. For instance, you will come across what is known as physical cosmology, religious cosmology, and modern metaphysical cosmology. As of late, more and more people are beginning to become interested in modern metaphysical cosmology. This type of cosmology can best be described as metaphysics and philosophy combined to study the totality of space and time. There are many ways that modern metaphysical cosmology is separated from the others listed above. Generally speaking, there are three questions that are addressed when it comes to this type of cosmology. They are as follows: 1. What is the main reason that the Universe exists? 2. What are the material components that the Universe is made up of? 3. Is the overall existence of the Universe a necessity? Where did it come from, and what is the cause of it? Over the years, many people have had different views on modern metaphysical cosmology. When it comes down to it, people who are interested in modern metaphysical cosmology address the questions listed above. And overall, these questions cannot be answered by looking deeper into science. As you can see, there is a lot that goes into modern metaphysical cosmology. If you thought that this subject was an easy one to understand, you can see by now that you are a bit off base. People have been studying cosmology for many years, and are yet to come up with any concrete answers. But all in all, this should not stop you from getting involved. As you learn more about modern metaphysical cosmology your viewpoints and opinions are sure to change. This is something that makes cosmology a fun subject to study. It is a great challenge, and one that up to this point that has been discussed time and time again.
Chemical Weapons
Chemical weapons are certainly not the same as conventional weapons since they deal with the use of toxic characteristics of certain chemical materials and are not as concerned about exploding things as is the case with conventional weapons. The aim of using chemical weapons is to destroy the enemy physically and also physiologically. In addition, it would be wrong to think about chemical weapons as a modern manmade invention because it has in fact been used from antiquity as well, though today’s such weapons are far more lethal than anything known to man till date. In fact, World War I certainly saw extensive use of chemical weapons and it even had a decided influence on the outcome of many battles, and in the process many casualties were inflicted on the opposing armies. That is why the Geneva Protocol made it unlawful to use chemical weapons in war and this Protocol was signed by almost every country in the year 1925. However, the use of chemical weapons has not been abolished because countries such as Italy have used them in wars in Ethiopia while the Japanese also used them against the Manchurians and also the Chinese despite having signed the Geneva Convention. Nevertheless, the Allies foreswore from deliberately using such weapons during the Second World War despite owning vast amounts of chemical weapons. Also, the chemicals used in the making of chemical weapons has also undergone many changes from the time of the First World War at which time the chemicals used consisted mainly of simple materials that were nothing worse than chemicals used in industrial use and those that were derived from such chemicals and these weapons were termed as classic chemical weapons. Of course, in more recent times, things such as mustard and phosgene as well as other agents have been used in making chemical weapons, and this was especially the case during the Second World War though thankfully such weapons were not used despite being amassed in huge quantities. There are also nerve gases used in chemical weapons whose action is much like that of pesticides and thus they are very lethal as well.
Thursday, December 31, 2009
Solar Energy
Tran 1 Solar Energy About 47 percent of the energy that the sun releases to the earth actually reaches the ground. About a third is reflected directly back into space by the atmosphere. The time in which solar energy is available, is also the time we least need it least - daytime. Because the sun's energy cannot be stored for use another time, we need to convert the suns energy into an energy that can be stored. One possible method of storing solar energy is by heating water that can be insulated. The water is heated by passing it through hollow panels. Black-coated steal plates are used because dark colors absorb heat more efficiently. However, this method only supplies enough energy for activities such as washing and bathing. The solar panels generate low grade heat, that is, they generate low temperatures for the amount of heat needed in a day. In order to generate high grade heat, intense enough to convert water into high-pressure steam which can then be used to turn electric generators there must be another method. The concentrated beams of sunlight are collected in a device called a solar furnace, which acts on the same principles as a large magnifying glass. The solar furnace takes the sunlight from a large area and by the use of lenses and mirrors can focus the light into a very small area. Very elaborate solar furnaces have machines that angle the mirrors and lenses to the sun all day. This system can provide sizable amounts of electricity and create extremely high temperatures of over 6000 degrees Fahrenheit. Solar energy generators are very clean, little waste is emitted from the generators into the environment. The use of coal, oil and gasoline is a constant drain, economically and environmentally. Will solar energy be the wave of the future? Could the worlds Tran 2 requirement of energy be fulfilled by the powerhouse of our galaxy - the sun? Automobiles in the future will probably run on solar energy, and houses will have solar heaters. Solar cells today are mostly made of silicon, one of the most common elements on Earth. The crystalline silicon solar cell was one of the first types to be developed and it is still the most common type in use today. They do not pollute the atmosphere and they leave behind no harmful waste products. Photovoltaic cells work effectively even in cloudy weather and unlike solar heaters, are more efficient at low temperatures. They do their job silently and there are no moving parts to wear out. It is no wonder that one marvels on how such a device would function. To understand how a solar cell works, it is necessary to go back to some basic atomic concepts. In the simplest model of the atom, electrons orbit a central nucleus, composed of protons and neutrons. Each electron carries one negative charge and each proton one positive charge. Neutrons carry no charge. Every atom has the same number of electrons as there are protons, so, on the whole, it is electrically neutral. The electrons have discrete kinetic energy levels, which increase with the orbital radius. When atoms bond together to form a solid, the electron energy levels merge into bands. In electrical conductors, these bands are continuous but in insulators and semiconductors there is an energy gap, in which no electron orbits can exist, between the inner valence band and outer conduction band [Book 1]. Valence electrons help to bind together the atoms in a solid by orbiting 2 adjacent nuclei, while conduction electrons, being less closely bound to the nuclei, are free to move in response to an applied voltage or electric field. The fewer conduction electrons there are, the higher the electrical resistively of the material. Tran 3 In semiconductors, the materials from which solar sells are made, the energy gap E.g. is fairly small. Because of this, electrons in the valence band can easily be made to jump to the conduction band by the injection of energy, either in the form of heat or light [Book 4]. This explains why the high resistively of semiconductors decreases as the temperature is raised or the material illuminated. The excitation of valence electrons to the conduction band is best accomplished when the semiconductor is in the crystalline state, i.e. when the atoms are arranged in a precise geometrical formation or “lattice.” At room temperature and low illumination, pure or so-called intrinsic semiconductors have a high resistively. But the resistively can be greatly reduced by doping,” i.e. introducing a very small amount of impurity, of the order of one in a million atoms. There are 2 kinds of doping. Those which have more valence electrons that the semiconductor itself are called donors and those which have fewer are termed acceptors [Book 2]. In a silicon crystal, each atom has 4 valence electrons, which are shared with a neighboring atom to form a stable tetrahedral structure. Phosphorus, which has 5 valence electrons, is a donor and causes extra electrons to appear in the conduction band. Silicon so doped is called n-type [Book 5]. On the other hand, boron, with a valence of 3, is an acceptor, leaving so-called holes in the lattice, which act like positive charges and render the silicon p-type[Book 5]. Holes, like electrons, will remove under the influence of an applied voltage but, as the mechanism of their movement is valence electron substitution from atom to atom, they are less mobile than the free conduction electrons [Book 2]. In a n-on-p crystalline silicon Tran 4 solar cell, a shadow junction is formed by diffusing phosphorus into a boron-based base. At the junction, conduction electrons from donor atoms in the n-region diffuse into the p-region and combine with holes in acceptor atoms, producing a layer of negatively-charged impurity atoms. The opposite action also takes place, holes from acceptor atoms in the p-region crossing into the n-region, combining with electrons and producing positively-charged impurity atoms [Book 4]. The net result of these movements is the disappearance of conduction electrons and holes from the vicinity of the junction and the establishment there of a reverse electric field, which is positive on the n-side and negative on the p-side. This reverse field plays a vital part in the functioning of the device. The area in which it is set up is called the depletion area or barrier layer[Book 4]. When light falls on the front surface, photons with energy in excess of the energy gap interact with valence electrons and lift them to the conduction band. This movement leaves behind holes, so each photon is said to generate an electron-hole pair [Book 2]. In the crystalline silicon, electron-hole generation takes place throughout the thickness of the cell, in concentrations depending on the irradiance and the spectral composition of the light. Photon energy is inversely proportional to wavelength. The highly energetic photons in the ultra-violet and blue part of the spectrum are absorbed very near the surface, while the less energetic longer wave photons in the red and infrared are absorbed deeper in the crystal and further from the junction [Book 4]. Most are absorbed within a thickness of 100 æm. The electrons and holes diffuse through the crystal in an effort to produce an even distribution. Some recombine after a lifetime of the order of one millisecond, neutralizing their charges and giving up energy in the form of heat. Others reach the junction before their lifetime has expired. There they are separated Tran 5 by the reverse field, the electrons being accelerated towards the negative contact and the holes towards the positive [Book 5]. If the cell is connected to a load, electrons will be pushed from the negative contact through the load to the positive contact, where they will recombine with holes. This constitutes an electric current. In crystalline silicon cells, the current generated by radiation of a particular spectral composition is directly proportional to the irradiance [Book 2]. Some types of solar cell, however, do not exhibit this linear relationship. The silicon solar cell has many advantages such as high reliability, photovoltaic power plants can be put up easily and quickly, photovoltaic power plants are quite modular and can respond to sudden changes in solar input which occur when clouds pass by. However there are still some major problems with them. They still cost too much for mass use and are relatively inefficient with conversion efficiencies of 20% to 30%. With time, both of these problems will be solved through mass production and new technological advances in semiconductors.
Bibliography
Tran 6
Bibliography
1) Green, Martin Solar Cells, Operating Principles, Technology and System Applications. New Jersey, Prentice-Hall, 1989. pg 104-106 2) Hovel, Howard Solar Cells, Semiconductors and Semimetals. New York, Academic Press, 1990. pg 334-339 3) Newham, Michael ,Photovoltaics, The Sunrise Industry, Solar Energy, October 1, 1989, pp 253-256 4) Pulfrey, Donald Photovoltaic Power Generation. Oxford, Van Norstrand Co., 1988. pg 56-61 5) Treble, Fredrick Generating Electricity from the Sun. New York, Pergamon Press, 1991. pg 192-195
Unification Theory
Unification Theory In particle physics, an attempt to explain all of the fundamental forces and their relationships between elementary particles in single framework was accomplished in theory by the g.u.t. by the grand unification theory. In relation to physics these forces can be described as fields that mediate interactions between separate or distant objects. These theories such as eltromagnetism and general relativity started to attempt the unification of theories, however they would emerge as the fundamental basics of the g.u.t. Or the grand unification theory. At sub atomic levels, these fields are described as quantum field theories, which started the ideas of quantum mechanics. In the 1940’s the ideas quantum electrodynamics (QED), the quantum field theory of electromagnetism, became fully developed. In QED, charged particles interact as they emit and absorb photons (minute packets of electromagnetic radiation), in effect exchanging the photons in a game of subatomic catch. This theory has become the prototype for theories of the other forces. During the 1960s and '70s particle physicists discovered that matter is composed of two types of basic building block--the fundamental particles known as quarks and leptons. The quarks are always bound together within larger observable particles, such as protons and neutrons. They are bound by the short-range strong force, which overwhelms electromagnetism at sub nuclear distances. The leptons, which include the electron, do not feel the strong force. However, quarks and leptons both experience a second nuclear force, the weak force. This force, which is responsible for certain types of radioactivity classed together as beta decay, is feeble in comparison with electromagnetism. At the same time that the picture of quarks and leptons began to crystallize, major advances led to the possibility of developing a unified theory. Theorists began to invoke the concept of local gauge invariance, which postulates symmetries of the basic field equations at each point in space and time. Both electromagnetism and general relativity already involved such symmetries, but the important step was the discovery that a gauge-invariant quantum field theory of the weak force had to include an additional interaction--namely, the electromagnetic interaction. Sheldon Glashow and peers independently proposed a unified electro weak” theory these forces based on the exchange of four particles: the photon for electromagnetic interactions, and two charged W particles and a neutral Z particle for weak interactions. During the 1970s a similar quantum field theory for the strong force, called quantum thermodynamics (QCD), was developed. In QCD, quarks interact through the exchange of particles called gluons. The aim of researchers now is to discover whether the strong force can be unified with the electro weak force in a grand unified theory (GUT). There is evidence that the strengths of the different forces vary with energy in such a way that they converge at high energies. However, the energies involved are extremely high, more than a million times as great as the energy scale of electro weak unification, which has already been verified by many experiments. Grand unified theories describe the interactions of quarks and leptons within the same theoretical structure. This gives rise to the possibility that quarks can decay to leptons and specifically that the proton can decay. Early attempts at a GUT predicted that the proton's lifetime must be in the region of 1032 years. This prediction has been tested in experiments that monitor large amounts of matter containing on the order of 1032 protons, but there is no evidence that protons decay. If they do in fact decay, they must do so with a lifetime greater than that predicted by the simplest GUTs. There is also evidence to suggest that the strengths of the forces do not converge exactly unless new effects come into play at higher energies. One such effect could be a new symmetry called supersymetry, which is part of the g.u.t.
Bibliography
i am the man
Observing Stars
Observing Stars Our view of the sky at night is possible because of the emission and reflection of light. 'Light' is the better-known term for the electromagnetic spectrum, which includes waves in the visible, ultra-violet, infra-red, microwave, radio, X-ray and gamma-ray regions. The scale of the spectrum is so large that no region is distinct, several overlap each other. Each of these regions in the electromagnetic spectrum represent transverse waves, travelling as electrical and magnetic fields which interact perpendicularly to each other, with different ranges of wavelength. The magnetic field oscillates vertically and the electric field horizontally, and each field induces the other. By the end of the nineteenth century, Maxwell gave a realistic value for c, the speed of light: c = __1__ = 3 x 108 ms-1 Ö(mo eo) The relationship between the speed of all electromagnetic radiation, wavelength (l) and frequency (f) is shown to be c = l f. Because the Universe is so vast, interstellar distances are so great that light emitted can take upwards of millions of years to reach us. Such large distances are often measured in ‘light-years’; one light-year (ly) is the distance travelled by a wave of light in a year. Because of the massive speed of light and distances, the light arriving at us would have left the object many years ago, so that looking at a far away star is much like looking back in time. Scientific observation of the stars is difficult because of the distorting effect of the Earth's atmosphere. One problem is atmospheric refraction-where light is bent. Turbulent air currents cause varying refractive indices, as there is no uniform air density. This causes an effect called scintillation, where stars appear to twinkle. The effect on regions of the electromagnetic spectrum other than the visible part, such as the absorption of certain frequencies by atmospheric chemicals, and the reflection of waves by charged molecules in the ionosphere, means that some spectral data is simply invisible to us on Earth. The Earth receives electromagnetic radiation of all wavelengths from all directions in space, but most of the electromagnetic spectrum is blocked out by the atmosphere well above the Earth's surface, where our eyes and instruments are mostly based. However, wavelengths from only two regions of the electromagnetic spectrum are able to penetrate the atmosphere. These two spectral windows in the atmosphere through which we can observe the Universe are called the optical window-which allows the visible wavelength region through; and the radio window-which includes the wavelength region from about 1 mm to 30 m. The telescopes used by astronomers on the ground are therefore classed as optical and radio telescopes. Optical telescopes work by either reflecting or refracting light, using lenses or curved mirrors to focus the light from a subject to form an image. Radio telescopes consist of a parabolic reflector and receiver on which the waves are focused. The gathering and resolving power depend on the diameter of the antenna. Radio observations are unaffected by the weather or time of day, and because of the larger wavelength of radio waves, dust in space and atmospheric convection currents are not a problem. Radio astronomy is used in the chemical analysis of elements (by emission and absorption spectra); to detect the motion of bodies due to the Doppler effect; and in investigation into the early Universe and the Big Bang. We can analyse radio waves from the centres of galaxies, including our own. Despite the radio window, there are still wavelengths that do not penetrate the atmosphere. Some radio waves are reflected from the ionosphere, part of the thermosphere, where streams of charged particles from the sun ionise gas molecules: this is photo-ionisation. Ultra-violet radiation, X-rays and gamma-rays are also absorbed at this layer. Absorption of the electromagnetic spectrum at various altitudes above Earth occurs to varying degrees. Much infra-red radiation does not reach ground level because of absorption in the upper atmosphere by water, and some carbon dioxide and oxygen molecules that lie between the ground and about 15 km of altitude (the troposphere). Ozone (tri-oxygen) and di-oxygen in the stratosphere absorbs much of the ultra-violet radiation (hence the ‘ozone layer’ at about 30km). A side effect of the ozone layer is that molecules re-radiate the energy in a few wavelengths of the green, red, and infrared regions, causing ‘airglow’. It is because of the limitations of Earth’s atmosphere, that astronomers learnt the benefits of observing from beyond it. Placing telescopes and instruments of mountain tops-to avoid clouds, bad weather and turbulence-or using balloons or aircraft, are useful, but satellites are far more so. All electromagnetic radiation can be detected, unaffected by absorption, reflection or refraction, dust, atmospheric haze, airglow, weather, light pollution or the time of day. The Hubble Space Telescope is probably the most famous astronomical satellite in orbit around Earth. Photographs taken by it have far improved detail than an Earth-based telescope. We have greater knowledge of elements and compounds present thanks to emission and absorption spectroscopy. The 1983 NASA Infra-Red Astronomical Satellite (IRAS) has been successful in infra-red observations across the sky, detecting nuclear and chemical reactions by spectrometry, and hot clusters where stars are born. The 1989 NASA Cosmic Background Explorer (COBE) satellite undertook a detailed study of background radiation: the ‘echo’ of the Big Bang. Low frequency microwaves present today are the result of the red-shift over a long time of the original, high-energy electromagnetic radiation from the time of the birth of the Universe. The future of satellite observations lies with X-ray and gamma-ray astronomy. X-ray images show where high-energy events occur, such as nuclear processes and matter entering a black hole. Gamma-rays are emitted from only the hottest and most violent bodies, and although difficult to detect, telescopes are used to map the Universe. Most observations surround the light from stars. There are billions of them in the Universe; we classify stars by their various characteristics. The properties of stars can be determined by the application of principles explained below. All stars visible to us must have surface temperatures high enough to emit light which we can see from so far away. Some appear brighter than others. The difficulty is in determining weather a star is very hot and bright, or not as bright but just much closer to us. We know that very hot things appear ‘red hot’ or even ‘white hot’, that the temperature of an object relates to the colour of light it radiates. The electromagnetic radiation emitted by any object (whatever its temperature) is known as thermal radiation. Hot objects such as stars emit high energy, high frequency radiation. At about 1000oc, thermal radiation falls in the visible region of the electromagnetic spectrum. To find out the temperature of a star, measurements need to be relative rather than absolute, as there is no possible way of measuring a star’s surface temperature physically! No object can perfectly emit (or absorb) light in practice, but it is useful to imagine such a body to make comparisons with: a ‘black body’. A black body is a perfect absorber of light; it follows therefore that it is also a perfect emitter of light. A perfect absorber would appear totally black; a perfect emitter would emit all radiation, including visible light, and would appear bright white. We know that a black body therefore emits a broad range of the electromagnetic spectrum. The most intense emission will peak at a particular wavelength. The hotter the body, the shorter the peak wavelength, but the higher the peak. Wein’s displacement law states that the peak wavelength, lmax , is inversely proportional to absolute (actual) temperature of an object. We assume that a star behaves as a black body. The relationship is shown below: lmax T = 2.898 x 10-3 m K Hence, we can relate the colour of a star to estimate its temperature, depending on where in the electromagnetic spectrum lmax lies. Astronomical objects have peak wavelengths ranging from radio to X-rays, i.e. surface temperatures from absolute zero to 107 K. It is apparent that the hotter an object is, the more intense the emission of radiation is. Luminosity (L) is the total power emitted by a body. The Stefan-Boltzmann law states that ‘the total energy radiated per unit time by a black body is proportional to the fourth power of its absolute temperature’; it also depends on the surface area (A): L = s A T4 Stefan’s constant (s) = 5.67 x 10-8 W m-2 K-4 The amount of power received per unit area is flux (equal to power / area). Light emitted from an object spreads out in all directions, the further away it gets the less intense it becomes according to the inverse square law: L = d-2 E.g., As Saturn is ten times the distance from the Sun as Earth, the intensity of radiation is receives is 1/100 th of that for Earth. The light reaching Earth from the sun can be analysed using a technique called spectroscopy. It is used to identify the chemical composition of stars (which is mostly hydrogen and helium), and their surface temperature. Once these are known, stars can be classified accurately. An emission spectrum is the spectrum of wavelengths of light emitted from atoms or molecules. They do this when they lose energy, which corresponds to a specific frequency of the electromagnetic spectrum. An atom or molecule may become electronically excited, electrons transfer to higher energy levels, and then later drop back to their normal, lower energy states, emitting this extra energy as photons of light in the process. Molecules gain translational, rotational, vibrational or electronic energy, depending on how much energy they first absorb. They must emit this quantised amount of energy again. Different elements and have different energy levels, this is why we can associate certain wavelengths with the physical behaviour of a particular atom. Even small molecules cannot withstand the high temperatures of stars, their spectra are only visible for cool stars. An absorption spectrum is apparent when wavelengths of light are missing against the continuous background of emitted light. These missing wavelengths have firstly been emitted from atoms in the inner layers of the star, but then absorbed by different chemicals in the outer layers. Thus we can identify the elements in the outer layers of a star. The Balmer series refers to the emission spectrum of hydrogen, specifically for high energy level electrons dropping back to the second energy level (n=2). Light emitted falls in the visible region of the electromagnetic spectrum, and the intensity of this light is an indication of a star’s surface temperature. The Balmer series is due to atoms being excited by kinetic collisions. The electrons of cool atoms occupy their ground state (n=1), as there are few collisions to excite the electrons. The hotter the atoms, the more energetic the collisions; more electrons are excited to even higher levels (n=3, 4,.etc). These electrons now absorb wavelengths beyond the Balmer series. The most intense Balmer emission spectra are from stars with intermediate surface temperatures at around 10 000K. Most electrons can absorb and re-emit wavelengths of the visible spectrum at this temperature. The light from stars travels very great distances, taking a long time, to reach Earth. Unsurprisingly, it can be affected by the time it reaches us. Of course, our nearest star is the Sun, and our nearest ‘neighbour’ is the moon. However, ‘near’ in space is nowhere near close enough to actually measure by hand. The first logical estimates used simple trigonometry in a method called parallax. This is where a distant object will appear at a different spot when viewed from a different angle. Simply, the position of a star is measured relative to the background, at the two times when the apparent distance between these viewing positions is as great as possible. As the Earth rotates around the Sun, with a radius of 1 astronomical unit (1AU = 1.496 x 1011 m), the greatest possible angle between two different views of a star is achieved at six month intervals, when the distance between these two times is 2AU: The further away the object, the smaller the parallax angle would be, as: Distance (d) = 1AU Tan (r) Distance (d) in parsec (pc) = _____________1_____________ Parallax angle (r) in arc-seconds Measuring parallax in this way is called annual parallax. It is suitable for objects up to about a distance of 100pc from us. Earth based instruments are less reliable as the parallax angle being measured gets smaller, greater measurements have been made by Earth orbiting telescopes such as 1989 ESA Hipparcus which avoid atmospheric limitations. We can only estimate the distances of more distant objects such as supernovae. One method is called spectroscopic parallax, where we can make the assumption that all stars are equally bright (although we know of course that they are not), and so the brighter a star the closer it is. The apparent magnitude (m) of a star is related to its intensity (I); its is an observational logarithmic scale. The absolute magnitude is a comparative scale based on the assumption that all objects are at a distance (d) of 10 pc. The two measurements are related: d = 10pc x 10 (m – M) / 5 The distance of an object is related to its intensity (using the inverse square law): I = L 4pD2 For objects further away than 10 megaparsecs, astronomers have made use of more unusual objects as reference points in the sky. Cepheid variable stars have luminosity which varies periodically. They vary in brightness as their surface temperature rises and falls. The absolute magnitude is directly proportional to the period, and using the above formula the distance of these stars can be calculated. These stars are present in distant galaxies, we can deduce how far away these are. Some supernovae behave in the same way. We know that stars and galaxies are moving away from us, because the spectra lines from some are shown to have been shifted. This is the Doppler effect, where the spectrum lines are displaced, because their wavelengths have been changed. The change in wavelength is related to the velocity: Df = Dl = v f l c The Doppler shift can occur when something is moving towards or away from us, however receding galaxies is evidence that our Universe is expanding (their light is shifted towards the red / longer wavelength part of the spectrum). It can also be used to determine the distance of an object from us. Hubble made the important finding that the further away a galaxy is, the greater its velocity. Also, all galaxies are generally moving apart from each other, including ours. Hubble’s law depends on the Hubble constant (Ho), but there is no accurate value for this, due to the inaccurate estimates for distances by other methods. v = Ho x d It is speculated that Ho lies between 40 and 100 km s-1 Mpc-1 The Doppler effect is also used to measure how fast stars and galaxies are rotating, and the orbital period of binary stars. A pair of binary stars each orbit a common centre of mass, as they are attracted by each other’s gravity. The stars usually have different masses, and will have different orbits (the radius of which is inversely proportional to the mass). When the stars are close to each other, it is difficult to distinguish between them, except by their different spectra (these are spectroscopic binary stars). Each is identified to be receding or approaching as they rotate, by Doppler shifting. We can find the combined mass of the two stars (M), based on Kepler’s third law of planetary motion: M = 4p2r3 GT2 G = Universal gravitational constant = 6.67 x 10-11 N m2 kg-2 The mass of each star can be calculated, as they are known to be in ratio of the distance to the centre of mass. We can see that there is so much to be discovered about the sky, over the years physicists have somewhat overcome the problem of sheer distance across the Universe. We have catalogued data about many stars, and crucially we can compare other stars to ones we already know about. We can learn how stars evolve from our observations, however we can only view a tiny part of history. Star populations are mapped on the Hertzsprung-Russell diagram, basically a graph of luminosity against surface temperature: From it we can examine the life sequences of a star, deduce a star’s absolute magnitude, and then their spectral class according to their surface temperature and other properties. We can identify what stage in its life a star it.
Bibliography
: ‘Astrophysics’, Nigel Ingham ; ‘Physics Passcards’, Graham Booth, Letts
Nuclear Energy And The Environment
Nuclear Energy and the Environment In our society, nuclear energy has become one of the most criticized forms of energy by the environmentalists. Thus, a look at nuclear energy and the environment and its impact on economic growth. Lewis Munford, an analyst, once wrote, Too much energy is as fatal as too little, hence the regulation of energy input and output not its unlimited expansion, is in fact one of the main laws of life. This is true when dealing with nuclear power. Because our societies structure and processes both depend upon energy, man is searching for the most efficient and cheapest form of energy that can be used on a long term basis. And because we equate power with growth, the more energy that a country uses, - the greater their expected economic growth. The problem is that energy is considered to have two facets or parts: it is a major source of man-made repercussions as well as being the basis of life support systems. Therefore, we are between two sections in which one is the section of resource availability and waste, and the other the continuity of life support systems pertinent to survival. Thus, the environmentalists believe that nuclear energy should not be used for various reasons. First of all, the waste product, i.e. plutonium, is extremely radioactive, which may cause the people who are working or living in or around the area of storage or use, to acquire leukemia and other cancers. They also show how billions of dollars are spent yearly on safety devices for a single reactor, and this still doesn't ensure the impossibility of a melt down. Two examples were then given of Chernobyl and Three Mile Island, in 1979, when thousands of people were killed and incapacitated. Finally, the environmentalists claim that if society wastes less energy, and develops the means to use the energy more efficiency, then there would be a definite decrease in the requirement for more energy producing plants. On the other hand, some business men and economists say that the present conditions should be kept intact, as the other forms of energy, e.g. oil, natural gas and coal, are only temporary, in dealing with surplus, and give off more pollution with less economic growth. Concurrently, countries wanted a more reliable, smokeless form of energy not controlled by OPEC, and very little uranium was required to produce such a high amount of resultant energy. Lastly, they said that renewable energy is (a) unreliable in that the wind, for example, could not be depended upon to blow, nor the sun to shine, and (b) were intermittent in that a 1,000 mega-watt solar farm may occupy about 5,000 acres of land, compared with less than 150 acres of land for a similar capacity nuclear power generation station. Because the energy technology that society employs directly influences the quantity and quality of life, the energy option that is chosen should have the greatest cost- benefit effectiveness as well as maximizing flexibility and purchases. However, those who believe in continuous energy consumption growth, seem to forget that there is only a limited supply of energy in every energy system, and to overdo any resource may provide for an unacceptable impact upon global and regional ecology. Thus, if the business world pushes the environment as far as it can go, Ceribus Paribus, please refer to figure 1. Thus, to use petroleum as a substitute for uranium, which is needed to power the nuclear system, would not be economically or environmentally sensible. I say this because, first of all, there is a major supply of uranium considering it was one of the last energy sources to be found as well as only a small amount of it is required to produce a lot of energy. Secondly, petroleum gives off carbon monoxide which is one of the reasons for ozone depletion; whereas, the uranium does not give off pollution except that it produces plutonium which needs to be buried for more than fifty years to get rid of its radiation. Finally, because so much of the petroleum will be required to power the vast area that nuclear energy can cover, the cost to us as the consumer would be massive! This would mean slower economic growth and/or expansion, especially when compared to nuclear energy. Therefore: Ceribus Paribus - (a) if the cost decreases, the demand increases, and - (b) if the cost increases, the demand decreases. Please refer to figures #2 and #3 respectively. Nuclear plants are now replacing coal burning plants. It will cost the taxpayers far more than they are currently paying for electricity. However, industrial officials claim that since the plants have useful lifetimes, they will save the consumers money in the long run. The problem with this is that this depends on hard to predict factors, such as the future price of oil and the national demand for electricity. It should also be noted that there is also a sharp jump in consumer costs when the plants are turned on to pay for the construction costs, plant manufacturers or other loan sources, plus interest. Thus, the cost of electricity may go up three-fold. New plants usually supply substantially more energy than the area requires; meaning that the consumer will be paying for this waste of energy, which is cost per kilowatt hour. It should also be noted that some plants are canceled during construction, which can raise the cost up to several billion dollars. This is absorbed by the government through tax laws, shareholders, and rate payers; and is considering the fact there is a continual rise in construction prices and a decrease in costs of alternative fuels, many utilities cancel plants, when almost half completed. (Late cancellation cost is an increase in the proportion to the amount that has been invested.) Albert Schweitzer, an ecologist wrote, nuclear power threatens the present and forecloses the future. It is unethical, and inferior to non-fission futures that enhance survival for humans, alive and yet to be born, and nature, with all its living entities. Therefore, in conclusion, it is clearly evident why nuclear energy should be abandoned, even though it may be considered as economically sound, and that we should concentrate more on conservation and quality rather than expansion as we have done in the past
Momentum
Conservation of Momentum Kristin Favreau October 26, 1999 Purpose: To show that momentum is conserved in a closed system by illustrating the conservation of momentum in an elastic collision and an inelastic collision. Method: If momentum is conserved in a closed system, the total momentum of the system before collision should equal the total momentum of the system after the collision. Strobe photos will be used in the calculations that will prove that momentum is conserved. 1.) Elastic collision: A strobe photo will be used that shows a large glider smashing into a smaller glider which is initially at rest. This will cause the smaller glider to move and the large glider will continue to move also. 2.) Inelastic collision: A strobe photo will be used that shows a glider smashing into another glider which is initially at rest. When they collide the two gliders will stick together and will move. -The masses, distances and times will be measured in order to calculate the momentums of the systems before and after collision occurs. Data: V = d/t P = m x v 1.) Elastic collision: When Mass Distance Time Velocity Momentum Glider A Before Collision .31215 kg .009m .6s .015 m/s .00468 Kg m/s Glider B Before Collision .15580 kg — — 0 m/s 0 Kg m/s Glider A After Collision .31215 kg .005m 1.0s .005 m/s .00156 Kg m/s Glider B After Collision .15580 kg .011m .6s .018 m/s .00280 Kg m/s 2.) Inelastic collision: When Mass Distance Time Velocity Momentum Glider C Before Collision .3105 kg .016m 1.0s .016 m/s .004968 Kg m/s Glider D Before Collision .3000 kg — — 0 m/s 0 Kg m/s Gliders C+D After Collision .6105 kg .015m 2.0s .008 m/s .004884 Kg m/s Calculations: 1.) Elastic collision: Before After Glider A .00468 Kg m/s .00156 Kg m/s Glider B + 0 Kg m/s +.00280 Kg m/s .00468 Kg m/s .00436 Kg m/s 2.) Inelastic collision: Total momentum before = Total momentum after mv + mv = (m + m ) v (.3105kg x .016 m/s) + 0 = (.3105 kg + .3000 kg) x .008 m/s .0050 Kg m/s = .0049 Kg m/s Conclusion: Through experiments with strobe photos involving elastic and inelastic collisions, I was able to show that momentum is contained within a closed system. My efficiency for the elastic collision was 3.54% and my efficiency for the inelastic collision was 1.01 %. Less than 10 % of the momentum was lost in either collision indicating a good experiment. The lost momentum can be attributed to the transfer from mechanical energy to thermal energy. Sources of Error: 1.) The distances measured in the two strobe photos were estimated. 2.) The measurement of time was an average. % error = difference x 100 sum of all 1.) % error = .00032 x 100 = 3.54 % error .00904 2.) % error = .0001 x 100 = 1.01 % error .0099
Metallic Conductor
Determination of r for a Metallic Conductor Aim: To determine the resistivity (r) of a given sample of wire Introduction: Physical factors that affect the resistance of a conductor are length, cross sectional area and a constant that depends upon the material called the resistivity. The resistance per unit length is the same all along a uniform wire so if the resistance of different lengths of a wire is found out, the resistivity can be calculated. Resistance of a material, R = Voltage / Current Resistance of a conductor, R = r × Length / Cross sectional area Apparatus: - 12V power supply - Power leads - 6 connecting leads - 2 crocodile clips - given sample of wire (» 5 m) - variable resistor – is used to alter the resistance to change the current and voltage for each length - ammeter – the 5 ampere outlet was used since the current was generally over 1 amperes - voltmeter – the 5 volt outlet was used because voltage was always below 5 volts - meter stick – more appropriate than a 30 cm ruler because the length is changed by 50 cm each time - micrometer – since the wire is very thin an accurate measurement of the diameter can be obtained by using a micrometer with an uncertainty of ± 0.0005mm. Diagram: Method: 1. Set up the apparatus as shown on the diagram. 2. Make sure the voltmeter outlet is at 5 volts and the ammeter outlet is at 1 amp. 3. Measure 50 cm of the wire using the meter stick. 4. Connect this part of the wire to the circuit using the crocodile clips. 5. Make sure the wire is not touching other parts of the wire. 6. Turn the power supply on, record the voltage and current. 7. Using the variable resistor, alter the resistance and take 4 more different readings of voltage and current for this length. 8. Repeat steps 4 to 6 for 5 more times, each time increase the length of wire by 50 cm using the meter stick. 9. Draw a graph of current against voltage for each length and find the resistance of each length by finding out the gradient of the graphs. 10. Measure the diameter of the wire using the micrometer. Take 3 reading at different places on the wire to reduce the uncertainty. 11. Calculate the cross sectional area of the wire, using the formula Area = p ´ radius2 12. Draw a graph of resistance against length. 13. Find the resistivity of the wire by finding the gradient of the graph and multiplying it by the cross sectional area. ( R = r L / A ) Results: Length (m)± 0.01 Voltage (volts)± 0.05 Current (amperes)± 0.05 0.5 0.70 1.15 0.5 1.30 2.00 0.5 1.90 3.10 0.5 2.45 3.90 0.5 2.90 4.70 Length (m)± 0.01 Voltage (volts)± 0.05 Current (amperes)± 0.05 1.0 0.55 0.40 1.0 1.05 0.85 1.0 1.60 1.25 1.0 2.50 1.95 1.0 4.05 3.10 Length (m)± 0.01 Voltage (volts)± 0.05 Current (amperes)± 0.05 1.5 0.80 0.40 1.5 1.50 0.80 1.5 2.45 1.30 1.5 3.80 1.90 1.5 4.50 2.30 Length (m)± 0.01 Voltage (volts)± 0.05 Current (amperes)± 0.05 2.0 0.90 0.35 2.0 1.30 0.50 2.0 2.20 0.85 2.0 3.40 1.30 2.0 4.30 1.65 Length (m)± 0.01 Voltage (volts)± 0.05 Current (amperes)± 0.05 2.5 1.20 0.35 2.5 1.40 0.45 2.5 2.35 0.75 2.5 3.35 1.00 2.5 4.70 1.45 Length (m)± 0.01 Voltage (volts)± 0.05 Current (amperes)± 0.05 3.0 1.00 0.25 3.0 1.70 0.45 3.0 2.80 0.75 3.0 3.80 1.00 3.0 4.90 1.25 Diameter of the wire: 1st reading = 0.709mm ± 0.0005 mm 2nd reading = 0.710mm ± 0.0005 mm 3rd reading = 0.710mm ± 0.0005 mm Analysis & Conclusion: Length (m)± 0.01 Resistance (ohms) 0.5 0.6161 ± 0.00071 1.0 1.306 ± 0.00098 1.5 1.985 ± 0.0025 2.0 2.618 ± 0.00046 2.5 3.263 ± 0.0052 3.0 3.883 ± 0.0049 Average diameter of wire = 0.710mm ± 0.0005 mm = 7.1 ´ 10 –4 m ± 5 ´ 10 –7 m Radius = 3.55 ´ 10 –4 ± 2.5 ´ 10 –7 = 3.55 ´ 10 –4 ± 0.0704 % Area = p ´ radius2 = p ´ (1.26 ´ 10 –7 ± 0.1408 %) = p ´ (1.26 ´ 10 –7 ± 1.77 ´ 10 –10) = 3.96 ´ 10 –7 m2 ± 5.57 ´ 10 –10 m2 Gradient of Resistance against Length graph = 1.307 1.307 = r / Cross sectional area = r / (3.96 ´ 10 –7 ± 5.57 ´ 10 –10 ) r = 5.176 ´ 10 –7 ± 7.28 ´ 10 –10 W m It was concluded from the experiment that the resistivity (r) of the wire is 5.2 ´ 10 –7 ± 7.3 ´ 10 –10 W m. Evaluation: - The actual value for the resistivity is 4.7 ´ 10 –7 W m. The resistivity value from the experiment is 5.2 ´ 10 –7, which is close to this value. - Resistivity is dependant on temperature and the temperatures in which these values were measured are not known. Since the uncertainty of the experimental value is very small, the difference between the values may be due to the temperature difference in which they were found. - Also, the purity of the metal wire is unknown. The metal may not be completely pure; there may be impurities in it and the experimental resistivity value may be different from the actual value because of this. - One of the uncertainties in the experiment was that it was very difficult to measure the length of the wire accurately. The wire was not straight and it was very hard to straighten it since it was very rigid. A new, straight wire should be used in order to avoid this inaccuracy. - The diameter of the wire was also difficult to measure because of the shape of the wire. Since it was twisted, it had dents in some parts and this made the reading inaccurate. This can also be avoided by using a straight wire and taking measurements from different parts of the wire. - In addition, the wire was not connected properly to the circuit since the crocodile clips touched only some parts of the wire. There should be better contacts to the wire; the wire should be surrounded completely. Soldering the contacts to the wire will minimize this uncertainty.
