110A
Physical Chemistry: Quantum Mechanics
Mid Term 4/27/09, 9:00 a.m. ;
allotted time: 50 minutes
Problem # 1: 20 pts
In addition to an uncertainty principle for position and momentum, there is one for
energy (E) and time (t): the product of the uncertainty of E and t is greater than or equal
to the Planck constant.
1.1
If the lifetime of an excited state of an atom is 10
9
sec., what is the uncertainty of the
energy of the state?
1.2
A nucleus in an excited state with lifetime 10
12
sec decays and emits a
γ
ray. What is
the uncertainty in the energy of the
γ
ray?
Problem # 2: 40
pts
The energies of a particle of mass m in a 1D box with walls at
0
and
a
, and V(x) = 0
inside the box are:
E = (h
2
n
2
)/ (8 m a
2
) ; n = 1, 2, ...; h is the Planck constant
The probability of finding the particle at a point x inside the box is:

Ψ
(x)
2
= (2/a) sin
2
(n
π
x/a)
2.1
What are the energies of a particle of mass m in a 1D box with walls located at
0
and
2a
, and those of a particle with walls located at
–a
and
a
?
2.2
What are the wavefunctions of a particle of mass m in a 1D box with walls located at
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 Fall '09
 Mccurdy
 Physical chemistry, pH, #, 8 m, 20 pts, 9 sec, 12 sec

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