Question

It is said that the photoelectric e?ect demonstrates the particle-like nature of light. Explain how this conclusion is reached. That is, what experimental evidence is consistent with particle-like behavior for light but not with wave-like behaviour? Cite at least two pieces of evidence. (b) Electrons with a speed of 2.0?106 ms1 pass through a double-slit apparatus. A detector measures interference fringes with a fringe spacing of 1.5 mm.
(i) What will the fringe spacing be if the electrons are replaced by protons having the same speed? (ii) What speed protons will produce interference fringes with a spacing of 1.5 mm? The mass of an electron is 9.11?1031 kg, whereas the mass of a proton is 1.67?1027 kg.
Part B (Advanced)
An electron in a one-dimensional potential energy well is found to have the wave function
(x)=Axe|x|/b,
where A is a normalisation constant and b is a constant (with units of length) that depends on the shape of the potential well.
(a) Sketch the probability density of the electron wave function.
(b) At what position or positions is the electron most likely to be found? Explain, and give an exact answer.

Answer 1

Classical wave theory could not explain the experimental evidence for photo-electric effect. The two instances where it was inconsistent are:

i] The intensity of the incident radiation on a metal is directly proportional to square of the electric field strength which means that a higher intensity will increase the electric field strength which in return would increase the force on each electron in the metal thereby increasing the kinetic energy of electrons ejected from the metal surface. However, the kinetic energy of the ejected electrons was not found to be proportional to the intensity of the incident radiation when the frequency of the radiation was below a threshold frequency.

ii] Energy of a wave is distributed over the entire wave and so even if ejection of electrons required a certain threshold energy, this energy will not be deposited instantaneously. This means that the electrons will not be ejected from the metal surface instantaneously. However, experimental evidence suggested that as long as the frequency of incident radiation was greater than the threshold, the electrons were ejected instantaneously which implied that the energy of light must be in discrete packets (photons).