17.7 The Intrinsic Angular Momentum of the Electron. “Spin” 761
b.The reduced mass of the nuclei in a CO molecule.
c.The magnitude of the orbital angular momentum of an
electron in a hydrogen atom in a state withn3,
l2,m1.
d.Thezcomponent of the orbital angular momentum in
part c.
e.Thezcomponent of the spin angular momentum of an
electron with “spin up.”
f.The magnitude of the spin angular momentum of an
electron.
g.The energy in electron volts of a hydrogen atom in the
n3 energy level.
h.The degeneracy of then3 energy level of a
hydrogen atom.17.49From the pattern of nodal surfaces observed in the
subshells that we have discussed, predict the following,
excluding the nodal sphere atr→∞:
a.The number of nodal spheres in the 6swave function.
b.The number of nodal spheres in a 6pwave function.
c.The number of nodal planes containing thezaxis in
the real part of theψ 6 d 0 (ψ 620 ) wave function.
d.The number of nodal cones in the real part of the
ψ 6 p 1 (ψ 611 ) wave function.
17.50Use the expression for the time-dependent wave function
to show that the real hydrogen-like energy eigenfunctions
correspond to standing waves, whereas the complex
hydrogen-like energy eigenfunctions correspond to
traveling waves. Tell how the traveling waves move.
Show that both types of energy eigenfunctions
correspond to stationary states.
17.51Identify the following statements as either true or false. If
a statement is true only under special circumstances, label
it as false.
a.The angular factorsΘandΦare the same functions
for the hydrogen atom wave functions and those of
any other central-force problem.
b.In a central-force problem, the motion of the center of
mass and the relative motion can be treated separately
only to a good approximation.
c.Every atom is spherical in shape.
d.Thexoryaxis could be chosen as the unique
direction for angular momentum components instead
of thezaxis.
e.The energy eigenvalues for the H atom in the
Schrödinger equation are identical with those in the
Bohr theory.
f. The angular momentum eigenvalues for the H atom in
the Schrödinger equation are identical with those in
the Bohr theory.
g.There is a one-to-one correspondence between the
states of the H atom in the Bohr theory and the states
of the H atom in quantum mechanics.