(a) (5 pts) Let the mass of the Sun be
m
S
and the mass of the earth
be
m
E
.
Write down the potential energy function for
V
(
r
) for
the Earth in the Sun’s gravitational field. Substitute this for the
Coulomb potential in our analysis of the hydrogen atom to com
pute the Bohr radius
a
for the EarthSun system.
Put in the
actual numbers to get a value for
a
in meters. Hint: It will come
out to a very small distance.
(b) (5 pts) As shown in Townsend (discussion around Eq. 10.50), the
most likely radius for an orbiting particle with quantum state
n
and maximal angular momentum
‘
=
n

1 (hence a nearly circular
orbit) is
r
=
n
2
a
. By putting in the actual EarthSun distance in
meters, use this to estimate the principle quantum number
n
for
the EarthSun system. Since the orbit of the Earth is described
very well by classical mechanics, you should find
n
1.
Notes for people using the first edition of Townsend
•
All the references to Townsend in this reading/HW assignment are the
same in the first and second editions.
3
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 Fall '15
 mechanics, Work, pts, Hydrogen atom, Townsend