Chapter 7, Problem 7.124SP

(a)

Interpretation Introduction

Interpretation:

The first three vibrational levels for $\text{HCl}$ has to be sketched.

(b)

Interpretation Introduction

Interpretation:

The energy needed to excite a $\text{HCl}$ from ground state to excited state has to be calculated.

Concept Introduction:

The energy of each photon is given as

$\text{E}\text{=}\text{hν}$

h is the Planck’s constant ($\text{6}\text{.63}\text{×}{\text{10}}^{\text{-34}}\text{J}\text{.s}$ ) which relates energy and frequency.

$\text{ν}$ is the frequency.

E is the energy of light particle.

The mathematical equation of various characteristics of light wave is given as follows,

$\text{c = νλ}$

C is the speed of light ($\text{3}{\text{.00 × 10}}^{\text{8}}\text{ m/s}$).

$\text{ν}$ is the frequency

$\text{λ}$ is wavelength.

(c)

Interpretation Introduction

Interpretation:

The vibrational nature of $\text{HCl}$ is not equal to zero at any temperature has to be justified using Heisenberg uncertainty principle.

Concept Introduction:

Heisenberg uncertainty principle:

It is not possible to identify both the particle’s momentum and position at same time with certainty.  And it given as mathematical equation

$\text{Δx}\text{Δp}\ge \frac{\text{h}}{\text{4π}}$

Where,

$\text{Δx}$ is uncertainty in position of particle

$\text{Δp}$ is uncertainty in momentum of particle.

h is Planck’s constant.