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Show that s → s transitions are not allowed in the hydrogen atom. To do this, show that the integral ∫ Ψ a ( s ) * O ⌢ Ψ b ( s ) d τ is exactly zero where O ⌢ is the operator representing the light. Assume that light has the symmetry species D u ( 1 ) in this completely spherical system.

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Physical Chemistry

2nd Edition
Ball + 3 others
Publisher: Wadsworth Cengage Learning,
ISBN: 9781133958437

Solutions

Chapter
Section
BuyFindarrow_forward

Physical Chemistry

2nd Edition
Ball + 3 others
Publisher: Wadsworth Cengage Learning,
ISBN: 9781133958437
Chapter 13, Problem 13.66E
Textbook Problem
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Show that s s transitions are not allowed in the hydrogen atom. To do this, show that the integral Ψ a ( s ) * O Ψ b ( s ) d τ is exactly zero where O is the operator representing the light. Assume that light has the symmetry species D u ( 1 ) in this completely spherical system.

Interpretation Introduction

Interpretation:

The given statement that ss transitions are not allowed in the hydrogen atom is to be validated. The value of integral Ψa(s)*OΨb(s)dτ is exactly equal to zero is to be stated.

Concept introduction:

The group of symmetry operations of which atleast one point is kept fixed is called point group. The symmetry operations can be identity, rotation, reflection, inversion and improper rotation.

Explanation of Solution

The symmetry of hydrogen is described by the Rh(3) point group. The irreducible representation of 1s orbital is represented by Dg(0). The irreducible representation of 2s orbital is represented by Dg(0). The light is represented by Du(1) symmetry species. It causes an electron to excite from 1s state to other state.

The table is taken from the Rh(3) character table as shown below.

ECϕiSϕσDg(0)11111Dg(0)11111Du(1)

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Chapter 13 Solutions

Physical Chemistry
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