1
Phy 3101 Modern physics, Spring 2008
Homework set week #13. Not Due at the start of class on Monday, April 7, 2008.
For numerical answers give two significant digits. The first should be correct, the second can
be approximate.
1. An astronomer finds an absorption line at λ= 164.1 nm in the ultraviolet region of
the sun’s continuous spectrum. He attributes the line to hydrogen’s Lyman series. Is
he right? Justify your answer.
2. The radius of the n= 1 orbit in the hydrogen atom is a0= 0.053 nm
(a) What is the radius of the n= 6 orbit?
(b) What is the radius of the n= 6 orbit of a singly ionized helium He+, which is
similar to hydrogen.
3. Assume that the angular momentum of the Earth in its motion around the sun is
quantized like the electron in a hydrogen atom according to
L=mvr =nh
2π=n¯h.
(a) What is the Earth’s quantum number n?
(b) How much energy would be released in the transition to the next lowest quantum
level?
(c) What would the change in the radius of the orbit be?
4. Light of wavelength 410.7 nm is observed in emission from a hydrogen source.
(a) To what series does this transition belong?
(b) What transition between Bohr orbits is responsible for this radiation?
5. Compute the de Broglie wavelength of each of the following particles with kinetic
energy Ekinetic = 4.5 KeV.
(a) An electron.
(b) A proton.
(c) An alpha particle.
6. A beam of electrons with kinetic energy 350 eV is incident on a KCl (potassium chlo-
ride) crystal whose planes of atoms are d= 0.315 nm apart. The beam of electrons
comes in at an angle θand “reflects” at the same angle θ.
Use the geometry as shown in
Fifth edition: figure 3-13 on page 135
Fourth edition: figure 3-16 on page 150
of the textbook.
(a) What is the de Broglie wavelength of an electron in the beam?
(b) Find al l of the angles θ, of the scattering maxima. Hint: this problem is phrased
to emphasize the similarity between the Davisson-Germer experiment and the
Bragg effect described on pages 147-149. You get 2 points for every correct
answer, and 1 point for every answer which is incorrect by a factor of 2.
