Chapter 11, Problem 11.14E

Interpretation Introduction

(a)

Interpretation:

The energy difference in $\text{J}$ between quantized energy levels for a hydrogen atom bonded to a surface acting as harmonic oscillator having classical frequency of $6.000\times {10}^{13}{\text{s}}^{-1}$ is to be calculated.

Concept introduction:

The energy of the harmonic oscillator is given by,

$E_n=\left(n+\frac{1}{2}\right)hv$

Where,

• $E$ is the energy.

• $n$ is the quantum number.

• $h$ is the Planck’s constant.

• $v$ is the frequency.

The total energy of the harmonic oscillator depends on the classical frequency and the integer $n$ of the system. The energy values are quantized as the energy values can be determined by this equation and $n$ can take only integer values between $0$ to infinity.

Interpretation Introduction

(b)

Interpretation:

The wavelength of light that must be absorbed by the hydrogen atom to go from one level to another is to be calculated.

Concept introduction:

The energy of the harmonic oscillator is given by,

$E_n=\left(n+\frac{1}{2}\right)hv$

Where,

• $E$ is the energy.

• $n$ is the quantum number.

• $h$ is the Planck’s constant.

• $v$ is the frequency.

The total energy of the harmonic oscillator depends on the classical frequency and the integer $n$ of the system. The energy values are quantized as the energy values can be determined by this equation and $n$ can take only integer values between $0$ to infinity.

Interpretation Introduction

(c)

Interpretation:

The region of the electromagnetic spectrum, to which the wavelength of light that must be absorbed by the hydrogen atom to go from one level to another belongs, is to be predicted.

Concept introduction:

Electromagnetic spectrum is the classification of the electromagnetic radiation according to their frequencies and wavelengths. This spectrum consists of gamma rays, X-rays, ultraviolet rays, visible region, microwaves and radio waves.

Interpretation Introduction

(d)

Interpretation:

An explanation of the results of parts a and b on the basis of the state of science in the early twentieth century is to be stated.

Concept introduction:

The energy of the harmonic oscillator is given by,

$E_n=\left(n+\frac{1}{2}\right)hv$

Where,

• $E$ is the energy.

• $n$ is the quantum number.

• $h$ is the Planck’s constant.

• $v$ is the frequency.

The total energy of the harmonic oscillator depends on the classical frequency and the integer $n$ of the system. The energy values are quantized as the energy values can be determined by this equation and $n$ can take only integer values between $0$ to infinity.