Chapter 7, Problem 7C.2ST

Interpretation Introduction

Interpretation:

The probability of finding electron of given energy in tunnel through the barrier of height of $\text{2}\text{eV}$ and width of $100pm$ 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 transmission probability for probability in 1-D barrier is determined by using the following expression,

$\begin{array}{c}T={\left\{1+\frac{{\left(e^{\text{κW}}-e^{\text{-κW}}\right)}^2}{16\epsilon \left(1-\epsilon \right)}\right\}}^{-1}\\ \text{κ}=\frac{{\left\{2m\left(V-E\right)\right\}}^{1/2}}{\hslash }\\ here,T=Transmissionprobability\\ m=mass\\ W=barrierwidth\\ V=barrierheight\\ E=energy\end{array}$