Discussion Problems
Due in section for weeks of Nov 1, and Nov 9, 2009
Problem 1
Discussion Problems # 9
7C staff
April 5, 2006
Problem 1
Find the solid angle (angular area) subtended by a sphere by computing the following integral:
Ω
sphere
=
d
Ω =
2
π
0
π
0
sin
θdθdφ.
Problem 2
Positronium is an exotic atom that consists of an electron and a positron orbiting one another.
a) Derive the reduced mass for positronium.
b) Derive the Bohr radius and allowed energies for positronium. (Hint: Be sure to use the results of part
a).)
c) How do the typical sizes of hydrogen and positronium compare? To answer this find the ratio,
a
0
p
/a
0
H
,
where
a
0
p
is the Bohr radius of positronium and
a
0
H
is the Bohr radius of hydrogen.
Problem 3
Tipler 456
If electric charge did not exist and electrons were bound to protons by the gravitational force to form
hydrogen, derive the corresponding expressions for
a
0
and
E
n
and compute the energy and frequency of
the
H
α
line and the limit of the Balmer series. Compare these with the corresponding quantities for “real”
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 Fall '08
 LIN
 Physics, Electron, Bohr radius, Positronium, positronium compare

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