Chapter 10, Problem 10.54E

Interpretation Introduction

Interpretation:

The probability that an electron will exist at the center of the box, approximated as $0.495a$ to $0.505a$, for the first, second, third, and fourth levels of a particle-in-a-box is to be calculated. The property of wavefunction apparent from these answers is to be stated.

Concept introduction:

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

${\Psi }_n(x)=\sqrt{\frac{2}{a}}\sin \frac{n\pi x}{a}$

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 ${\Psi }^2$. For the normalization of the wavefunction, the wavefunction is integrated as a product of its conjugate over the entire limits.