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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
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
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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