Download Practice Exam No. 3

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Physics 250
Practice Exam III
1. A particle of mass m moves in a three-dimensional box with sides L. If the particle is in the
2
third excited level, corresponding to n = 11 , find (a ) the energy of the particle, (b) the
combinations of n 1 , n 2 , and n 3 that would give this energy, and (c) the wavefunctions
for these different states.
2. A hydrogen atom is in the 6g state. (a) What is the principal quantum number? (b) What is
the energy of the atom? (c) What are the values for the orbital quantum number and the
magnitude of the electron’s orbital angular momentum? (d) What are the possilbe values for
the magnetic quantum number? For each value, find the corresponding z component of the
electron’s orbital angular momentum and the angle that the orbital angular momentum vector
makes with the z axis.
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3.
The figure shown presents the ionization energy as a function of Z for the elements.
25
He
Ionization energy (eV)
Ne
20
Ar
Kr
15
Xe
Rn
Hg
10
5
Ti
Li
Na
8
0
8
10
Rb
K
Cs
18
20
18
30
40
32
50
60
70
80
90
Atomic number, Z
(a) What is the complete electron coniguration for Li, Na, K, He, Ne, Ar ?
(b) Identify on the graph the region of Z where the 3d subshell is being filled, where the 4p
subshell is being filled, where the 4d and 5p subshells are being filled.
(c) For which values of Z between Z = 15 and Z = 50 are the combined electron
wavefunctions completely isotropic, i.e. spherically symmetric?
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4. The electron of a H e atom is in the 3d state.
(a) What is the principal quantum number and what is the energy of the state
(b) What is the orbital quantum number and the magnitude of the electrons orbital angular
momentum (in units of h )?
(c) What are the possible values of the magnetic quantum m l . For each value, what is the Z
component of the orbital angular momentum in units of h ?
(d) What are the possible values of the total angular momentum j ?
(e) If the atom is placed in a magnetic field of 1 Tesla, what are the possible photon energies
for transitions to the 2p state (you may ignore the electron spin)?
(f) What is the wave function of the 3d electron if m l = – 1 ?
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5.
Calculate the average expectation value for the potential energy of an electron in the ground
state of hydrogen.
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