linear rigid molecule to z-polarized microwave radiation. Show explicitly that the YO → Yº tational transition is allowed while the Y→ Y₂ transition is not allowed. TABLE 6.3 The first few spherical harmonics. Y = Y₂ Y₂¹ = 1 3 87 5 167 15 8.7 15 327 1/2 sin be 1/2 1/2 (3 cos² 0 - 1) sincos de-i 1/2 sin de Y = 1/2 x₁¹ = (2²)" 15 Y = (2) 15 32π X=(3 cos@ 1/2 1/2 sin gel sin cos e 1/2 sin² 0e²

Chemistry: The Molecular Science
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Chapter7: Molecular Structures
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1. Refer to the Table below that lists the first few spherical harmonics YM. Suppose we subject
a linear rigid molecule to z-polarized microwave radiation. Show explicitly that the Y→ Yº
rotational transition is allowed while the Yo Yo transition is not allowed.
TABLE 6.3
The first few spherical harmonics.
YOU
1
(4x)¹/2
3
Y₂¹
Y₂²
1/2
Y =
87
1/2
x² = (15) (3 cos² 0-1)
1/2
=
sin Be
15
87
15
327
sin cos Be-¹
1/2
sin² Be-24
Y₁ =
Y₁¹ =
3
87
15
87
Y₂ =
Y² = (3
15
1/2
32π
cos 9
1/2
1/2
sin gel
sin cos e
1/2
sin² 0e²
Transcribed Image Text:1. Refer to the Table below that lists the first few spherical harmonics YM. Suppose we subject a linear rigid molecule to z-polarized microwave radiation. Show explicitly that the Y→ Yº rotational transition is allowed while the Yo Yo transition is not allowed. TABLE 6.3 The first few spherical harmonics. YOU 1 (4x)¹/2 3 Y₂¹ Y₂² 1/2 Y = 87 1/2 x² = (15) (3 cos² 0-1) 1/2 = sin Be 15 87 15 327 sin cos Be-¹ 1/2 sin² Be-24 Y₁ = Y₁¹ = 3 87 15 87 Y₂ = Y² = (3 15 1/2 32π cos 9 1/2 1/2 sin gel sin cos e 1/2 sin² 0e²
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