Part a (a) it is said that the photoelectric effect 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 2.0x 10° m s- 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 speed? replaced by protons having the same (ii) what speed protons will produce interference fringes with a spacing of 1.5 mm? the mass of an electron is 9.11 x 10-31 kg, whereas the mass of a proton is 1.67 x 10 27 kg. part b (advanced) an electron in a one-dimensional potential energy well is found to have the wave function (x)= are-l1/b where a is a normalisation constant and b is a constant (with units of length) that depends shape of the potential well. on the (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.