Question

A 50 electron is trapped between electrostatic walls 200eV high. How far does its wave function extend beyond the walls?

Short answer

Electron wave extent beyond the walls $\delta =1.59\times {10}^{-11}m$.

Step-by-step solution

Wave function

Know that, how far the wave function goes beyond the boundaries of the room so utilise the depth of penetration equation.

$\delta =\frac{\sout{h}}{\sqrt{2m(u_o-E)}}...................\left(1\right)$

Known values are,

E = 50 ev,

U_o= 200eV.

The electron wave beyond the wall.

From the electron volt to joule to convert E and U_o

Multiply by them 1.60218x10^-19 then E = 8.0109x10^-18 joule and U_o= 3.204x10^-17 joule.

Substitute (1) into,

$$\begin{gathered} \delta =\frac{1.0545\times {10}^{-34}}{\sqrt{2\times 9.1093\times {10}^{-31}\times \left(3.204\times {10}^{-17-8.0109\times {10}^{-18}}\right)}} \\ \delta =1.59\times {10}^{-11}m \end{gathered}$$

So, the electron wave beyond the wall is $\delta =1.59\times {10}^{-11}m$.