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Phy 3031 Modern physics, Spring 2007
Homework set #9. Due at the start of class on Wednesday, March 7, 2007.
For numerical answers give two significant digits. The first should be correct, the second can
be approximate.
1. The wavelength of a particular line in the Balmer series is measured to be 379.1 nm.
What transition does this correspond to?
2. 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.
3. 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.
4. 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?
5. 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?