Chapter 7, Problem 7C.3ST

Interpretation Introduction

Interpretation:

The energy separation between the given levels of an electron trapped in a square cavity with sides of length $1nm$ has to be calculated.

Concept Introduction:

The wave function is considered to be normalized if the probability of finding the particle in considered domain is equal to 1 and therefore, the integral function of given wave function in considered domain is equal to 1.

The energy difference between adjacent levels in one dimensional box is determined by using the following equation.

$\begin{array}{c}\Delta E=E_{n+1}-E_n\\ =\left(2n+1\right)\frac{h^2}{8m{L}^2}\end{array}$

The energy separation between two given levels are determined by using following expression,

$\begin{array}{c}{E}_{nX,nY}=\left(n^2{}_X+n^2{}_Y\right)\frac{h^2}{8m{L}^2}\\ here,L=length\\ m=mass\\ h=Planck\text{'}sc\text{onstant}\\ n_X\&n_Y=Energylevels\end{array}$