Physics 200
Homework #6
Due: November 2, 2005
1. The wavelength limits of the visible spectrum are often quoted as 400 nm to 700 nm.
Express the energy corresponding to these wavelengths in electronVolts (eV).
E = hf = hc/ and we know that hc = 1240 eV nm
For 400nm E = hc/ = 1240eVnm/400nm = 3.1 eV
For 700nm E = hc/ = 1240eVnm/700nm = 1.8 eV
2. The work function for molybdenum is 4.22 eV.
(a) What is the threshold wavelength for the photoelectric effect in this metal?
We know that the maximum kinetic energy of the electron that is knocked off the metal is
MaxK.E. = hf – W
We can rewrite W (the work function) as W = h fthreshold = hc/threshold
So threshold = hc/W = 1240 eV nm / 4.22 eV = 294 nm
(b) What is the stopping voltage if light of 200 nm is used?
eVstopping = maximum KE of the electron = hf – W = hc/ – W
To find using wavelength:
eVstopping = hc/ – W = 1240eVnm/200nm - 4.22eV = = 6.20 eV – 1.98 eV = 4.22 eV
3. The threshold wavelength for potassium is 558 nm.
(a) What is the work function for potassium?
The photons have just barely enough energy to knock off the electrons, so the electrons
really don’t have any kinetic energy once they’re knocked off.
maximum KE of the electron = 0 = hf – W = hc/ – W
hc/ – W = 0
W = hc/ = 1240eVnm/558nm = 2.22 eV
(b) What is the stopping voltage when light of 400 nm is used?
eVstopping = hc/ – W = 1240eVnm/400nm - 2.22eV = = 3.10 eV – 2.22 eV = 0.88 eV
4. X-rays with a wavelength of 0.02000 nm are scattered through 90 degrees by an
electron. The wavelength of the scattered x-rays is measured to be 0.02243 nm. What is
the recoil energy of the electron in eV?
The total initial energy is equal to the total final energy
E electron initial + E photon initial = E electron final + E photon final
The electron is initially at rest so: E electron initial = 0
0 + hc/ initial = E electron final + hc/ final
E electron final=hc/ initial - hc/ final=1240eVnm/0.02000nm – 1240eVnm/0.02243nm
= 62000 eV – 55283 eV = 6717 eV = energy given to the electron from the photon
Homework #5
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