Chemistry 455 A
Autumn 1998
Reinhardt, Gibbons and Caralombous
No Calculators of any type may be used on this exam!
Each student may have one (1) handwritten 5 by 8 inch note card.
Note that all answers must be supported by “work clearly shown”, or a
an explicit explanation in words of how the result was arrived at!
Exam #1.v.1 (100 points)
Name: _________________________________________
UW
ID#:_______________________________________
Signature: ______________________________________
Points
Problem #1______________________
Problem #2______________________
Problem #3______________________
Total
_____________________
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Problem #1.
20 points.
The Bohr atom.
This problem is from your homework.
The energy of an electron in the n
th
Bohr orbit for a nucleus of atomic number “Z” is
E
=

Z
2
m e
4
/(8
ε
o
2
h
2
n
2
)
We are approximating
μ
by m = electron mass.
(15 points) Using the formula above, derive the
general “Rydberg Balmer” formula:
1/
λ
=
Z
2
R ( 1/n
2
 1/m
2
)
and arrive at an explicit expression for the Rydberg constant R, in terms of the fundamental constants,
h,e,c,m,
π
,
ε
ο
……
(5 points) State in words how and why you have used the BohrEinstein frequency relation in your
derivation.
Hint, it might be helpful to draw an energy level diagram.