   # Draw (at least roughly) plots for the first five wavefunctions for the particle-in-a-box. Now draw the probabilities for the same wavefunctions. What similarities are there between the wavefunctions and their respective probabilities? ### Physical Chemistry

2nd Edition
Ball + 3 others
ISBN: 9781133958437

#### Solutions

Chapter
Section ### Physical Chemistry

2nd Edition
Ball + 3 others
ISBN: 9781133958437
Chapter 10, Problem 10.52E
Textbook Problem
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## Draw (at least roughly) plots for the first five wavefunctions for the particle-in-a-box. Now draw the probabilities for the same wavefunctions. What similarities are there between the wavefunctions and their respective probabilities?

Interpretation Introduction

Interpretation:

The plots for the first five wavefunctions and probabilities for the particle-in-a-box are to be drawn. The similarities between the wavefunctions and their respective probabilities are to be stated.

Concept introduction:

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

Ψn(x)=2asinnπxa

Where,

n is the number of energy level.

a is the width of the box.

The probability for particle in a box is taken as the square of the wavefunction and is denoted by Ψ2.

### Explanation of Solution

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

Ψn(x)=2asinnπxa

Where,

n is the number of energy level.

a is the width of the box.

The plot for the first five wavefunctions for the particle-in-a-box is shown in figure 1.

Figure 1

The probability for particle in a box is taken as the square of the wavefunction and is denoted by Ψ2. The plot for the first five probabilities for the particle-in-a-box is shown in figure 2.

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