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Phy 3031 Modern physics, Spring 2007
Homework set #7. Due at the start of class on Wednesday, February 21, 2007.
For numerical answers give two significant digits. The first should be correct, the second can
be approximate.
1. The cosmic microwave background radiation fits the black-body distribution for a
temperature T = 2.7 K.
(a) What is the wavelength of the maximum intensity in the spectrum?
(b) What is the frequency of the radiation at the maximum?
(c) What is the total power incident on the Earth from this background radiation?
2. A 40 W incandescent light bulb radiates from a filament at a temperature T = 3300 K.
Assume that the filament radiates like a black body.
(a) What is the wavelength of the radiation at the maximum in the spectrum?
(b) What is the frequency of the radiation at the maximum?
(c) Assume that λm is a good estimate of the average wavelength of the photons
radiated. About how many photons does the filament radiate every second?
(d) If you are standing 5 m away and are looking at the filament, then how many
photons enter your eye every second? Assume that the diameter of your pupil is
5 mm.
3. The work function of molybdenum is 4.22 eV.
(a) What is the threshold frequency for the photoelectric effect in molybdenum?
(b) Will yellow light of wavelength 560 nm eject photoelectrons from molybdenum?
4. The Compton effect has a photon scattering off an electron. This may be observed
with photons of wavelength 0.07 nm.
(a)
(b)
(c)
(d)
(e)
What is the energy of such a photon?
What is the wavelength of a photon scattered at 180◦ ?
What is the energy of a photon scattered at 180◦ ?
What is the recoil energy of the electron if the photon is scattered at 180◦ ?
For an incident photon of frequency f , what is the maximum amount of kinetic
energy that the recoiling electron can gain via Compton scattering?