Chapter 10, Problem 10.47E

Interpretation Introduction

(a)

Interpretation:

The wavelength of light corresponding to $1.00\times {10}^{-32}\text{J}$ energy is to be stated. The comparison of this wavelength to the diameter of the Earth, which is $1.27\times {10}^7\text{m}$, is to be shown.

Concept introduction:

The energy for particle in a box is given by the expression as follows.

$E=\frac{n^2{h}^2}{8m{a}^2}$

Where,

• $E$ is the energy of the particle

• $n$ is the number of energy level

• $h$ is Planck’s constant

• $m$ is the mass of the particle

• $a$ is the width of the box

The expression of the energy for particle in a box involves $n$ which shows that the energy is quantized for a particle in a box.

Interpretation Introduction

(b)

Interpretation:

The width of a box that an electron needs to be in, to possess $1.00\times {10}^{-32}\text{J}$ energy is to be calculated.

Concept introduction:

The energy for particle in a box is given by the expression as follows.

$E=\frac{n^2{h}^2}{8m{a}^2}$

Where,

• $E$ is the energy of the particle

• $n$ is the number of energy levels

• $h$ is Planck’s constant

• $m$ is the mass of the particle

• $a$ is the width of the box

The expression of the energy for particle in a box involves $n$ which shows that the energy is quantized for a particle in a box.