Chapter 8, Problem 8A.1AE

(i)

Interpretation Introduction

Interpretation:

The orbital degeneracy of the levels in a hydrogen atom having energy $-hc{\tilde{R}}_{\text{H}}$ has to be calculated.

Concept introduction:

Orbital degeneracy plays an important role in the quantum mechanics.  Orbital represents the number of quantum levels of equal energy.  Therefore, the number of equal energy states gives the value of orbital degeneracy.  The value of orbital degeneracy cannot be negative.  Orbital degeneracy is represented by $n^2$.

(ii)

Interpretation Introduction

Interpretation:

The orbital degeneracy of the levels in a hydrogen atom having energy $-\frac{1}{9}hc{\tilde{R}}_{\text{H}}$ has to be calculated.

Concept introduction:

Orbital degeneracy plays an important role in the quantum mechanics.  Orbital represents the number of quantum levels of equal energy.  Therefore, the number of equal energy states gives the value of orbital degeneracy.  The value of orbital degeneracy cannot be negative.  Orbital degeneracy is represented by $n^2$.

(iii)

Interpretation Introduction

Interpretation:

The orbital degeneracy of the levels in a hydrogen atom having energy $-\frac{1}{25}hc{\tilde{R}}_{\text{H}}$ has to be calculated.

Concept introduction:

Orbital degeneracy plays an important role in the quantum mechanics.  Orbital represents the number of quantum levels of equal energy.  Therefore, the number of equal energy states gives the value of orbital degeneracy.  The value of orbital degeneracy cannot be negative.  Orbital degeneracy is represented by $n^2$.