Wave-Particle Duality + Special Relativity Flashcards
When was Newton’s corpuscular theory?
1670s
When was Huygens’ wave theorgy?
1690s
What were the details of Newton’s theory?
Light is made of ‘corpuscles’ - particles which are perfectly elastic, rigid, weightless, and travel in straight lines
What were the details of Huygens’ theory?
Light is made of waves, with wave fronts made from secondary wavelets.
Why was Newton’s theory initially preferred?
He was the more famous scientist.
How did Newton’s theory address reflection?
Corpuscles would bounce off surfaces
How did Huygens’ theory address reflection?
Wavelets would be reflected
How did Newton’s theory address refraction?
Corpuscles attracted to boundary, travel faster in a denser medium (wrong!!!)
How did Huygens’ theory address refraction?
Waves travel slower in denser media (correct!!)
What could Huygens’ theory not explain?
Nothing!
What could Newton’s theory not explain?
Diffraction, interference, polarisation
When was Young’s double slit experiment?
1801
When was wave theory accepted, and why?
1850s+, corpuscular theory could not explain polarisation.
What happened in Young’s double slit experiment?
Light going through 2 slits formed a pattern of fringes - waves could make this by superposing either constructively or destructively, but is not possible to explain with the corpuscular theory.
What is a black body?
A body that emits all wavelengths of radiation possible at a given temperature.
What is the ultraviolet catastrophe?
Prediction where most light would be emitted at short wavelengths - exponentially increasing at ultraviolet. Doesn’t happen.
What law explains the absence of the ultraviolet catastrophe?
Planck’s interpretation of waves, where E = hf and travel in quanta.
What did Planck suggest?
All radiation is emitted or absorbed in quanta (photons)
Photons are not corpuscles
Energy of the quantum depends on frequency of the radiation, E = hf
No ultraviolet catastrophe as higher frequency photons carry more energy
How did Einstein explain the observations of the photoelectric effect?
Using photons - needing both wave and particle explanations depending on what phenomenon was being observed
What photoelectric observation was explained by wave theory? (ignore)
More intense radiation leads to more photoelectrons emitted per second - as more energy ‘accumulated’ by metal, so more electrons.
What photoelectric observation could be explained by quanta and wave theory - quanta explanation.
More intense rad = more photoelectrons per second - more photons absorbed by metal, so more electrons.
What was the explanation for the photoelectric threshold frequency?
Minimum frequency = minimum energy of PHOTON = work function, could not be a wave as intensity had no effect on work func.
What was the explanation for the instantaneous emission of electrons in the photoelectric effect?
Using quanta, electrons emitted soon as photon absorbed - not a wave as that would take time to deposit energy.
What was the explanation for the range of kinetic energies present in the photoelectric effect?
Range of kinetic energies up to a maximum, using quanta Ek = hf - work func.
How can you find work function from stopping potential?
Work function is the intercept of stopping potential against frequency. Threshold frequency is when stopping pot. = 0
How does a high intensity affect photocurrent?
Increases it, as a higher intensity wave means more photoelectrons per second.
What is the setup to measure stopping potential?
Vacuum with a window to transmit UV light into it, and an anode and cathode. Then by using a variable power supply you can find stopping potential at a certain frequency of light, by changing v until no light makes it through the vacuum.
What was the speed of light thought to have been before Fizeau’s experiments?
Infinite
What was Fizeau’s experiment?
A toothed wheel with n teeth at a distance d between mirrors. Wheel span at frequency f.
What did Fizeau find?
That when spinning his wheel at frequency f light JUST got through the gap, so c = 4dnf.
What are the two postulates of Einstein’s theory of special relativity?
Physical laws have the same form in all inertial frames
The speed of light in free space is invariant (shown by Michelson-Morley)
What is an inertial frame of reference?
A reference frame moving at a constant velocity (i.e no acceleration)
What are the equations relevant to wave-particle duality?
wavelength = h/p = h/(meV)^0.5
What are de Broglie’s equations?
mv x lambda = h
What does increasing V do for low-energy diffraction experiments? (voltage)
Increases energy and so speed of the electrons
Decreases the de broglie wavelength
Produces rings in a diffraction pattern which are brighter and have a smaller radius
What was the Michelson-Morley experiment designed to do?
Measure the impact of the aether, a theoretical medium for the transmission of light. Did not exist, returned a null value.
What was the prediction of the Michelson-Morley expeiment?
That light would move more slowly when Earth is moving ‘against’ the aether than with it. Would manifest as a shift in an interference pattern.
What did the Michelson-Morley experiment prove?
Light is not affected by the earth’s motion, so the speed of light is constant.
What was the setup for the Michelson-Morley experiment?
Monochromatic light source was split into two by a semi-silvered glass block. Then moves away and recombines - if any slowing was present in one direction it would manifest as an interference pattern.
Why do electron microscopes have such a high resolving power?
Because the wavelength of an electron is much less than the wavelength of visible light.
What is the mode of operation for a TEM?
Beam of electrons passes through a sample, resolution about 10^-10m
What is the mode of operation for a STM?
Fine-tipped probe scans the surface, resolution about 10^-12m
Where is an image formed on a TEM?
Fluorescent screen
How is an image formed on an STM?
Using the P.D produced when the height is kept constant - or using the height over time when the P.D is constant.
What are TEMs focused with?
Magnetic lenses, deflection depends on speed
What is the detail of a TEM limited by?
Lens aberration, slight variations in the speed of electrons.
What is the detail of an STM limited by?
The resolution of measuring instruments
What did Hertz use to discover radio waves?
High voltage sparks jumping across air to produce radio waves. Detected using a loop of wire with a gap, detecting mag field as it causes P.D changes and so a spark across the gap.
What did Hertz find about radio waves?
The speed by using the wavelength;
The frequency, and that c = f theta
That they were polarised by a change in signal strength when he rotated the dipole.
What did Maxwell predict?
The existence of self-propagating waves of oscillating magnetic and electric fields (EM waves). Predicted speed too, validated by Fizeau.
What is the equation for time dilation, and what do the symbols represent?
t = t(0) / root(1-(v^2/c^2)). t0 is proper time, stationary with respect to the clock. T is the time measured by an observer with speed V relative to the clock - time moves more slowly for them.
What is the equation for length contraction, and what do the symbols represent?
l = l0(root(1-(v^2/c^2)). L0 is proper length (stationary with respect to the clock). L is the length measured by observer with speed v relative to the clock.
What is the equation for mass and energy in special relativity?
E = m0c^2 / root(1-(v^2/c^2)), kinetic energy. At zero speed E = moc^2, rest energy. At speed v, Ek = mc^2 - moc^2
What is the equation for mass in special relativity?
m = m0 / (1-(v^2/c^2)).
What is the evidence for time dilation and length contraction?
Muon decay - more muons went further through the atmosphere than would be expected given their half-live; turns out they were moving close to the speed of light so time dilated and length contracted so they went further.
What is the evidence for mass and energy under special relativity?
Bertozzi measured k.e of electrons at different speeds, getting results within 10% of predicted values.
How do mass and energy increase as the speed approaches c?
Exponentially, so is impossible to actually reach c.
What parts of the photoelectric effect couldn’t be explained by wave theory?
Threshold frequency doesn’t work as wave theory suggests any freq = emission
Immediate emission contradicts wave theory
Increasing intensity does not increase speed as predicted by wave, but increases per sec.
Photoelectrons have range of k.e
How did Einstein explain the Photoelectric effect?
Photons - packets with particley interactions. All energy transferred when a photon interacts with an electron. Explains WF.
Energy instantly transferred.
Intensity = photons per second. So more photons = more interactions/s.
All electrons get same amount of energy, yet deeper in metal will lose due to collisions == range of k.e
What was the setup of the Michelson-Morley experiment?
2 beams of light perp. to each other forming an interference pattern - idea is one would be slowed by aether so rotating apparatus would change interference pattern.
