Chapter 20, Problem 14P

(a)

Interpretation Introduction

Interpretation: The moment of inertia I of HCl needs to be calculated in ${\text{kg m}}^{\text{2}}$ .

Concept Introduction:

The moment of inertia, I for HCl can be calculated using the following formula:

  $I=\frac{h}{8{\pi }^{2}B}$

Here, h is Planck’s constant and B is Rotational constant.

(b)

Interpretation Introduction

Interpretation: The energies (in J) of the rotational levels J =1, 2 and 3 from J =0 state needs to be calculated for HCl.

Concept Introduction: For a molecule, the energy of J-state can be calculated using the following formula:

  $E_J=BhJ\left(J+1\right)$

Here, B is rotational constant, h is Planck’s constant and J is rotational levels.

(c)

Interpretation Introduction

Interpretation: The bond length for H-Cl needs to be calculated in angstroms.

Concept Introduction: For a molecule, the moment of inertia, Iis related to bond length as follows:

  $I=\mu r^2$

Here, $\mu$ is reduced mass and r is bond length.

(d)

Interpretation Introduction

Interpretation: The initial and final J states need to be calculated for the observed absorption lines.

Concept Introduction: The frequency for the transition from J to J+1 level is represented as $2B\left(J+1\right)$ .

Here, B is rotational constant.