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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
= nh̄.
2π
(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 chloride) crystal whose planes of atoms are d = 0.315 nm apart. The beam of electrons
comes in at an angle θ and “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 all 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.
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7. A radar transmitter used to measure the speed of pitched baseballs emits pulses of
2.0 cm wavelength that are 0.25 µs in duration.
(a) What is the length of the wave packet produced?
(b) To what frequency should the detector be tuned?
(c) What must be the minimum bandwidth of the receiver?
8. You are given the task of constructing a double slit experiment for 5 eV electrons.
(a) If you wish for the first minimum of the diffraction pattern to occur at 5◦ , what
must be the separation of the slits?
(b) How far from the slits must the detector be located if the first minima on either
side of the central maximum are to be separated by 1 cm?
9. A neutron in an atomic nucleus is bound to other neutrons and protons in the nucleus
by the strong nuclear force when it comes within about 1 fm of another particle.
(a) What is the approximate minimum kinetic energy of a neutron localized within
a box 1 fm on a side?
(b) What would be the minimum kinetic energy of an electron localized within a box
of the same size?