11.38. Show that V, and ¥, for 2-D rotational motion are orthogonal. (You may want to use Euler's theorem.)
11.38. Show that V, and ¥, for 2-D rotational motion are orthogonal. (You may want to use Euler's theorem.)
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11.38
Transcribed Image Text:does not move. Comment on the difference, anc
assuming the
compare the difference to that found in Example 11.10.
11.6 2-D Rotations
11.36. Why can't the quantized values of the 2-D angular
momentum be used to determine the mass of a rotating sys-
tem, like classical angular momentum can?
11.37. Show that V of 2-D rotational motion has the
same normalization constant as V13 by normalizing both
wavefunctions.
11.38. Show that V, and V, for 2-D rotational motion are
orthogonal. (You may want to use Euler's theorem.)
at
11.39. Show that the 2-D rotational motion wavefunctions
have no nodes. (Hint: Evaluate the expression for probability
and check its dependence on 4.)
at
ll
11.40. What are the energies and angular momenta of the
first five energy levels of benzene in the 2-D rotational motion
approximation? Use the mass of the electron and a radius of
1.51 Å to determine I.
in
11.41. A proton rotates in a circle of radius 5.00 X 10 1 m.
What are the first three rotational energy levels?
r?
ng
11.42. A 25-kg child is on a merry-go-round/calliope, going
around and around in a large circle that has a radius of
8 meters. The child has an angular momentum of 600 kg-m2/s.
(a) From these facts, estimate the approximate quantum
number for the angular momentum the child has. (b) Estimate
the quantized amount of energy the child has in this situation.
How does this compare to the child's classical energy? What
ay
of
ar-
principle does this illustrate?
11.43. Using Euler's identity, rewrite the first four 2-D rotational
wavefunctions in terms of sine and cosine
g it.
crion for the ener
2.n rigid
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