Question

A helium atom is in a finite potential well. The atom’s energy is$1.0\mathrm{eV}$below ${\mathrm{U}}_0$. What is the atom’s penetration distance into the classically forbidden region?

Short answer

The penetration depth is$\approx 2{\mathrm{A}}^0.$

Step-by-step solution

Given information

We have given,

the energy difference =$1\mathrm{eV}$

We have to find the penetration distance.

Simplify

We know the penetration distance write as,

$$\begin{gathered} \mathrm{\eta }=\frac{\mathrm{h}}{2\mathrm{\pi }\sqrt{2\mathrm{m}({\mathrm{U}}_{\mathrm{o}}-\mathrm{E}})} \\ \mathrm{\eta }=\frac{6.63\times {10}^{-34}}{2\mathrm{\pi }\sqrt{2\times 9.1\times {10}^{-31}\mathrm{kg}(1\times 1.6\times {10}^{-19}\mathrm{J})}} \\ \mathrm{\eta }=1.95{\mathrm{A}}^0 \\ \mathrm{\eta }\approx 2{\mathrm{A}}^0 \end{gathered}$$