Sample Test Problems

1. What is the maximum wavelength of electromagnetic radiation which can eject electrons from a metal having a work function of 3 eV? (3 points)
   Answer
   The minimum photon energy needed to knock out an electron is 3 eV. We just need to convert that to wavelength.
   $$\begin{eqnarray*} E&=&h\nu=3 eV \\ \nu&=& {c\over\lambda} \\ {2\pi\hbar c\o... ...over 3 eV}&=&{2\pi (1973 eV\AA) \over 3 eV}\approx 4000 \AA \\ \end{eqnarray*}$$
   
   
   
   

2. * Based on classical electromagnetism and statistical mechanics, Rayleigh computed the energy density inside a cavity. He found that, at a temperature T, the energy density as a function of frequency was
   
   $$u(\nu,T) = {8\pi\nu^2\over c^3} k_B T .$$
   
   
   Why is this related to black body radiation? Why was this in obvious disagreement with observation?
3. What is the maximum wavelength of electromagnetic radiation which can eject electrons from a metal having a work function of 2 eV?
4. * State simply what problem with black-body radiation caused Plank to propose the relation $E=h\nu$ for light.
5. The work function of a metal is 2 eV. Assume a beam of light of wavelength $\lambda$ is incident upon a polished surface of the metal. Plot the maximum electron energy (in eV) of electrons ejected from the metal versus $\lambda$ in Angstroms. Be sure to label both axes with some numerical values.