CHEM 132B Study Guide - Quiz Guide: Wave Function, Angular Momentum OperatorExam
Course CodeCHEM 132B
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Chem 132B Practice Quiz 1 Key
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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
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
a) Calculate the energy of the electron in J.
y) = 13h2
8meL2= 7.832 ×10−19 J.
b) How many states have the same degenerate energy?
c) Is there any chance of ﬁnding the electron outside of the box?
d) What do you expect would happen to the probability of ﬁnding the elec-
tron outside of the box if we keep the potential outside high but ﬁnite?
Now there is a ﬁnite chance of ﬁnding the electron outside of the box.
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