11.29.11 Discussion Section Questions; Simple Quantum Calulations and the Heisenberg
Uncertainty Principle
1)
Consider an electron in a 3d orbital in hydrogen
a)
For an electron in this orbital, give the quantum numbers:
If more than
one quantum number is possible, give all possible values.
Answer: for 3d, n=3. The letter d indicates
. The quantum number m
l
has five
possibilities
b)
Calculate the orbital energy of an electron in the 3d orbital of hydrogen. How
many orbitals have this energy?
Answer:
Five orbitals have this energy. That is, 3d orbital state is fivefold degenerate.
c) Calculate the orbital angular momentum of a 3d electron. You can give your
answer in units of
.
Answer:
c)
Calculate the values for the z components of the angular momentum Lz. Here also
you can give you answer in units of
:
Answer:
d)
Extra Problem: Using your results from parts c and d, sketch the quantized
orientations of the 3d electron’s orbital
angular momentum. It is OK to give a flat
sketch with lengths in units of
.
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 Fall '12
 Chiu
 Electron, Heisenberg Uncertainty Principle, Werner Heisenberg, orbital angular momentum, Schroedinger

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