1. The photoelectric threshold wavelength of a tungsten surface is 270 nm. Calculate the
maximum kinetic energy (in eV) of the electrons ejected from this tungsten surface by
ultraviolet radiation of frequency 1.45 × 1015 Hz.
2. What would the min. work function for a metal have to be for visible light (380–750 nm)
to eject photoelectrons?
3. The cathode-ray tubes that generated the picture in early color televisions were sources of
x-rays. If the acceleration voltage in a television tube is 15 kV, what are the shortestwavelength x-rays produced by the television?
4. (a) What is the minimum potential difference between the filament and the target of an xray tube if the tube is to produce x-rays with a wavelength of 0.16 nm? (b) What is the
shortest wavelength produced in an x-ray tube operated at 30 kV?
5. A laser produces light of wavelength 620 nm in an ultrashort pulse. What is the minimum
duration of the pulse if the minimum uncertainty in the energy of the photons is 1%?
6. An x-ray with a wavelength of 0.1 nm collides with an electron that is initially at rest. The
x-ray’s final wavelength is 0.119 nm. What is the final kinetic energy of the electron?
7. An ultrashort pulse has a duration of 7.2 fs and produces light at a wavelength of 522 nm.
What are the momentum and momentum uncertainty of a single photon in the pulse?
8. (a) An electron moves with a speed of 4.5 × 106 m/s. What is its de Broglie wavelength?
(b) A proton moves with the same speed. Determine its de Broglie wavelength.
9. An electron has a de Broglie wavelength of 2.79 Å. Determine (a) the magnitude of its
momentum and (b) its kinetic energy (in joules and in electron volts).
10. (a) A nonrelativistic free particle with mass m has kinetic energy K. Derive an expression
for the de Broglie wavelength of the particle in terms of m and K. (b) What is the de Broglie
wavelength of an 800-eV electron?
11. What is the de Broglie wavelength for an electron with speed (a) v = 0.469c and (b) v =
0.958c? (Hint: Use the correct relativistic expression for linear momentum if necessary.)
