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CHEM 132B Study Guide - Quiz Guide: Wave Function, Angular Momentum OperatorExam


Department
Chemistry
Course Code
CHEM 132B
Professor
Eric Potma
Study Guide
Quiz

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Chem 132B Practice Quiz 1 Key
Name (Last, First):
Student ID number:
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Problem 1
Encircle all that are true.
a) Because an electron is small and has wave-like properties, its energy states
are automatically quantized. False
b) Wavefunctions can have amplitude in regions where there is no classical
probability of finding a particle. True
c) A quantum mechanical system cannot be in two eigenstates of an operator
at the same time. False
d) The operator for energy is called the Hamiltonian. True
Problem 2
An electron is trapped in a 2D square box with sides L= 1 nm. Inside the box
we have V= 0 while outside V=. The electron is in an eigenstate of the
Hamiltonian and the wavefunction is given as:
Ψ(x, y) = 2
Lsin 3πx
Lsin 2πy
L
a) Calculate the energy of the electron in J.
E=h2
8meL2(n2
x+n2
y) = 13h2
8meL2= 7.832 ×1019 J.
b) How many states have the same degenerate energy?
2
c) Is there any chance of nding the electron outside of the box?
No
d) What do you expect would happen to the probability of nding the elec-
tron outside of the box if we keep the potential outside high but nite?
Now there is a nite chance of nding the electron outside of the box.
1
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