Turning Points


Electrons - Cathode Rays

  • A discharge tube is a tube with a negative electrode (cathode) and a positive electrode (anode) inside a tube with a low pressure gas. 
  • When a high voltage is applied across a gas at a low pressure, the gas emits light. The colour of the light is characteristic of the gas inside the tube. 
  • The pressure of the gas could be reduced by using a vacuum pump. This resulted in the gas remaining dark when a high voltage was applied but the anode glowed. This lead to scientists concluding that some ray was being emitted at the cathode travelling towards the anode. They named them cathode rays.
  • It was then proven that the rays were made up of charged particles with mass by deflecting the rays in magnetic and electric fields.
  • The high potential difference causes the gas to glow because a strong electric field is produced which ionises the gas atoms. The low pressure then allows these positive ions to be accelerated towards the cathode, on contact with the cathode, they cause a large number of electrons to be knocked off the surface. 
  • These 'knocked off' electrons then accelerate towards the anode, and when colliding with gas atoms, cause the atoms to ionise or become excited to higher energy levels. The subsequent de-excitation causes the emission of visible and UV light.
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Electrons - Thermionic Emission

  • Thermionic emission is a method of freeing electrons from a metal in order to create cathode rays. It can create a cathode ray without the electrons torn from atoms in a gas.
  • The work function of a metal is the minimum energy needed to remove a delocalised electron from the surface of the metal. 
  • When a cathode is electrically heated, some of the electrons gain enough thermal energy (greater than or equal to the work function) to overcome the attractive forces in the metal and can escape from the surface of the metal.
  • An evacuated tube containing an electron gun which creates a high speed electron beam from thermionic emission is known as a cathode ray tube (CRT).
  • A high voltage between the anode and the heated cathode creates an electric field in which electrons are accelerated. 
  • Increasing the anode-cathode pd means the electrons gain more speed. 
  • A directly heated cathode means there is a higher rate of thermionic emission; an indirectly heated cathode can operate at temperatures lower than direct emission.
  • Increasing the current supplied causes more electrons to be released per second.
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Electrons - Calculating v of Electrons from Thermi

  • The work done on a charged particle is given by eV. The kinetic energy is equal to work done, assuming the electron has negligible kinetic energy when ejected from the cathode, so eV=1/2 mv^2
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Electrons - Specific Charge

  • The specific charge of an electron (e/m) can be determined by the balanced field method or the fine beam tube method.
  • The balanced field method uses perpendicular electric and magnetic fields. The two fields would deflect the electron in opposite directions therefore when there is no deflection of the electron, the force due to the electric field is equal to the force due to the magnetic field. The force due to the electric field is Ee (where E is electric field strength) and causes the electron to follow a parabolic path towards the positive plate; the force due to the magnetic field is Bev. Therefore, where Ee = Bev, v = E/B and 1/2 mv^2 = ev, it follows then  e/m = v^2/2V and then substitute v for E/B.
  • The fine beam tube method uses the equation mv^2/r = Bev to determine e/m
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Electrons - Milikan's Oil Drop Experiment

  • Once the ratio of e/m was found, it was possible to estimate the order of magnitude size of charge. 
  • The atomiser created a fine mist of oil droplets within an electrically insulated chamber. Some charged by friction as they left the atomiser.
  • Some particles fell through the top plate into view of the microscope, then when a voltage is applied between the two plates, the force on the droplet due to the electric field could be altered so the droplet was held stationary so mg = EQ.
  • To determine the Q of the oil drop, mass must be determined first by using m = Vρ. 
  • The radius was determined by using the terminal speed and Stokes' law (which determines the viscosity of air and therefore the resistive force due to viscosity).
  • mg = 6πηrv (where η is the coefficient of viscosity, r is radius and v is terminal speed), therefore since m = Vρ, r = (9ηv/2ρg)^1/2
  • By repeating the experiment many times, Millikan found that values for Q were always multiples of 1.6x10^-19. Therefore he deduced that charge did not exist in quantities less than this and must be the magnitude of charge on an electron.
  • Whether the droplet was negatively or positively charged, the quantity of charge was the same so e is now referred to as the fundamental charge.
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Wave-Particle Duality - Corpuscular Theory of Ligh

  • Newton's theory of light proposed that light is made up of particles or corpuscules. 
  • Huygens proposed that, instead, light is a longitudinal wave that propagates through the ether. In Huygen's principle states that all points on a wave front act as point sources for secondary wavelets that spread out in the direction of the wave.
  • Newton's theory could account for sharp shadows and theorised that different colours were created by different coloured corpuscules. His theory's explanation for therefraction of light depended on the fact that light travelled faster in a medium than in air, due to the medium exerting an attractive force, increasing its component of velocity perpendicular to the surface. 
  • Huygen's theory could account for relection and refraction but was unable to explain sharp shadows. His theory suggested that waves moved slower in a medium than in air.
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Wave-Particle Duality - Young's Double Slit

  • Until Young's experiment, it was generally assumed that Newton's corpusular theory was correct.
  • The double slit experiment, an interference pattern was formed from two slits producing two coherent sources of light. This defied Newton's theory as he would have expected two single bright fringes rather than an interference pattern.
  • This led to acceptance that light has wave properties and, after it was proven that light travelled slower in water medium than in air, the discarding of Newton's corpuscular theory. 
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Wave-Particle Duality - Speed of Light

  • Fizeau's experiment measured the speed of light in air and obtained a value only 5% from the currently accepted value.
  • He shone a light at a distant mirror several km away, through a toothed wheel. The frequency of the wheel could be changed and when the wheel was turned, the light was split into bursts due to the tooths of the wheel obstructing the path of the light. When the wheel reached a specific frequency, the pulse of light leaving one gap returned when it was completely blocked by the consecutive tooth, so no light was seen through the partially reflecting mirror. 
  • t = T/2N (where t is the time for the wheel to turn through a distance equal to one tooth, T is the time for the wheel to complete one full rotation and N is the number of teeth on the wheel)
  • t = 1/2Nf
  • c = 2D/t
  • c = 2D/(1/2Nf) = 4DNf
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Wave-Particle Duality - EM Waves

  • Electromagnetic waves were theorised by Maxwell when it was found than a current in a wire, results in an electric field being induced, then a B-field is induced, then an E-filed is induced and so on.
  • Maxwell's theory led to the equation:
  •  (http://maxwells-equations.com/equations/speed-of-light.gif)
  • μ = permittivity of free space (relates to electric field)
  • ε = permeability of free space (relates to B-field)
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Wave-Particle Duality - EM Spectrum

  • The EM spectrum is made up of 7 regions, each with their own characteristics.
    • Radio - 0.1m-1km, used in radio transmissions.
    • Microwaves - 1mm-0.1m, used in radar, tv transmissions and cookery.
    • Infrared - 100nm-1mm, used in heat detectors, remote controls and optical fibres.
    • Visible - 400-700nm, used in optical fibres and is the range of eye sensitivity.
    • Ultraviolet - 1nm - 100nm, used in fluorescence and security markings.
    • X-ray - 0.1pm-10nm, used for medical and dental imaging, airport security and cancer treatment.
    • Gamma - 0.1fm-0.1nm, used for irradiation, sterilisation and cancer treatment.
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Wave-Particle Duality - Hertz and Radio Waves

  • Hertz's spark transmitter experiment showed how a recieving loop of wire produced a spark when placed near a high voltage circuit with two capacitors emitting a spark across a gap. The spark produced across the first circuit lead to a current being induced in the loop and therefore a spark over the gap in the loop.
  • Hertz then furthered his experiments with radio waves to reflect with a metal sheet, focus with a concave reflector and pass through some materials.
  • He also set up a stationary wave, which was used to determine a value for the speed of an EM wave. As the reciever loop was moved along the line of the transmitter, the intensity of the sparks varied from a maximum to minimum (nodes and antinodes). The distance between nodes is half a wavelength and the frequency is determined by the transmitter. The wave equation can then be used.
  • Hertz was also able to demonstate the polarisation of EM waves. When the recieving loop is perpendicular to the antenna, no spark was created because no emf wis induced in the loop. An EM wave emitted from a straight antenna only has an electric field parallell to the antenna.
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Wave-Particle Duality - UV Catastrophe

  • Black body radiation is the concept of a perfect absorber and emitter of radiation. The dominant wavelength at a given temperature is indicative of the temperature of the body and at higher temperatures, falls in the range of the visible spectrum.
  • However, this was where the UV catastrophe emerged as it became clear that these classial physics theories could not account for the intensity reducing after peak wavelength, so the amount of UV radiation for all hot objects was infinitely large.
  • Max Planck solved this problem by suggesting that EM wave energy was quantised, dependent on frequency, giving rise to the equation E = hf.
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Wave-Particle Duality - The Photoelectric Effect

  • The photoelectric effect is evidence for the particle nature of electromagnetic radiation. When a light or UV source is directed at the surface of a metal, electrons may be released.
    • Electrons are not emitted if the light is below a threshold frequency.
    • Electrons are emitted immediately if the light exceeds the threshold value.
    • Electrons are ejected with a range of kinetic energies, the light frequency determines the kinetic energy. The intensity of light only affects the number of electrons emitted.
  • If light were a wave, the energy would be able to build up with each wave front, so eventually electrons would be released.
  • The wave theory is also unable to explain the existence of a threshold frequency.
  • Einstein called a quantum of light energy a photon and proposed that to escape the surface of a metal, an electron must gain a specific amount of energy, the work function. The frequency correlated to this energy = hf, is the threshold frequency and any extra enegy is converted to kinetic energy,
  • Ekmax =hf -  φ
  • Millikan confirmed this equation by plotting a graph, using the stopping potential of the electrons to calculate the kinetic energy.  
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Wave-Particle Duality - Wave-Particle Duality

  • Neither the wave theory nor photon theory can describe fuly what light is. Therefore it has wave-particle duality.
  • The Compton effect confirms Einstein's hypothesis that photons have momentum, given by ρ = E/c.  However, given that a photon has no mass, this did not make sense.
  • De Broglie combined Einstein's equation with Planck's energy equation to form the equation E = hc / λ.
  • De Broglie then put forward a hypothesis that all matter can act as a wave, called matter waves, with the associated wavelength, λ = h/p (where p is momentum and h is the Planck constant).
  • This hypothesis was verified by electron diffraction in 1927. It was shown that a fine beam of electrons fired at a thin sheet of atoms were spread and at certain angles had a maximum intensity, similar to an interference pattern. 
  • Circular rings may also be formed by electron diffraction through a crystal structure. A larger wavelength gives more diffraction so the rings are more widely  spaced. But if the speed of the electrons is increased (by increasing anode pd) the wavelength decreases resulting in a more tightly spaced ring pattern,
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Wave-Particle Duality - TEM

  • Transmission Electron Microscope
    • The electrons pass through a number of magnetic lenses: the first is a focussing lens, then the electron passes through the specimen (where more elctrons are passed through where it is thin and fewer where it is thicker), the next set of lenses act to reduce the diffraction effect of the specimen on the electrons, the projector lens then magnifies and flips the image onto a fluorescent screen.
    • Higher resolutions are achieved where ther is as little diffraction as possible, this is achieved with higher electron speeds, as it reduces their wavelength.
    • However, the loss of speed of the electrons due to the specimen which means the lenses will not be able to focus all of the electrons to the same point, also the loss of speed results in an increase in wavelength, therefore increaseing diffraction. The sensitivity of the microsope also means it must be protected from slight vibrations.
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Wave-Particle Duality - STM

  • Scanning Tunnelling Microscope
    • The STM creates images using an effect called quantum tunnelling which allows some electrons from either the sample or the probe to 'jump the gap' at a distance of about 1 nm creating an electric current.
    • The closer the gap, the higher the probability of the electrons jumping the gap so the higher the current.
    • The STM works by either maintaining a constant height and a changing current or maintaining a constant current and a changing height.
    • This tunnelling effect depends on the wave nature of electrons as they have a finite probability of jumping the gap at a small distance, somparable to the wavelength.
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Special Relativity - Michelson-Morley Experiment

  • The ether was a concept hypothesised by Young, thought to act as a medium for EM waves to travel through. It was postulated as a fixed background, against which absolute motion could be measured.
  • Michelson and Morley's experiment set out to measure the difference in speed between parallel and perpendicular beams of light to determine the absolute speed of the Earth relative to the ether, as the speed of light woud be affected by the 'ether wind' created by the Earth.
  • The interferometer consisted of plane mirrors perpendicular to one another and a partial mirror to split the light. A compensator plane of glass was also used to adjust for refraction.
  • When the two beams return to the viewing telescope, they form an interference pattern as they undergo superposition. 
  • The existence of the ether could have been proven if, when rotated, there was a small shift in interference pattern as this would show that the speeds of the two beams was different. 
  • However, no shift in the interference pattern was found, a null result. This demonstrated that the speed of light was invariant and that absolute motion and the ether did not exist.
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Special Relativity - Einstein's Theory

  • Einstein's theory of special relativity set out two postulates:
    • Physical laws have the same form in all inertial frames of reference.
    • The light of light in a vacuum is invariant which means that light always travels at the same speed.
  • Time Dilation:
    • A clock moving relative to an observer would appear to run more slowly.
    • The time observed by the observer of the moving clock is the proper time t0 and can be used when the triangle derivation gives rise to the equation t = t0 (1-v^2/c^2)^-1/2 (where t is the time observed by the moving observer, v is the velocity and t0 is the proper time observed by the stationary observer)
    • (1-V^2/c^2)^-1/2 is also known as the Lorentz Factor and can be given the symbol γ.
  • Length Contraction:
    • This theory predicts that the length of a moving object appears shorter to an observer in the direction of its motion.
    • l = l0 γ 
  • These phemomena are only seen in situations in which the speed of the moving object is notably close to the speed of light (i.e above ~0.3c and raises exponentially as it gets close to the speec of light.
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Special Relativity - Muon Decay

  • Muon decay provides evidence for the effect of time dilation.
  • A geiger counter can be used to measure the intensity of cosmic muons at the top of a mountain and at the base; from this the difference in intensity and the half life of the muons can be used to show that a significantly higher number of muons reached the base than would be expected. Indicating that the rlativistic half life of the muons is longer, allowing less decay to occur and more muons reach the base before decay.
  • This can occur because the muons reach speeds close to the speed of light ~99.6%c.
  • Time passes more slowly for the muons than the Earth-based observer, therefore, they have a relativistic half life of more than 1.5μs.
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Special Relativity - Mass and Energy

  • Relativistic mass, m = γm0 (where m0 is the mass in an inertial frame of reference i.e rest mass)
  • This equation predicts that at speeds close to the speed of light, the amount of force needed to accelerate further becomes significantly larger, so the mass increases.
  • Approaching the speed of light, the mass of an object becomes infinitely large, hence no object can reach the speed of light. 
  • Evidence for this theory came from accelerating electrons and determining their specific charge.
  • E = mc^2 (where m is relativistic mass) and the equation for realativistic mass in terms of m0 can be substituted into this equation to give E = γm0c^2
  • Because mass and energy are directly linked, the principle of conservation of energy becomes the principle of conservation of mass-energy.
  • For a particle accelerated to speeds close to the speed of light, E = KE + RestE = QV + m0c^2
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Special Relativity - Bertozzi's Experiment

  • Bertozzi set out to investigate the relationship between velocity of an electron and its kinetic energy. 
  • He used a Van de Graff generator to accelerate electrons until they hit a metal disc which then calculated the kinetic energy by specific heat capacity and tmeperature change.
  • A graph of v^2/c^2 was presented and showed that the results verified Einstein's predictions, the kinetic energy continued to increase as the speed of light was near, and the speed approached a limiting value.
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