Question

Calculate the reflection probability $\mathbf{5}\mathit{e}\mathit{v}$for an electron encountering a step in which the potential drop by $\mathbf{2}\mathit{e}\mathit{v}$

Short answer

The reflection probability is $0.007$

Step-by-step solution

Definition of Reflection Probability

Reflection probability or reflection coefficient is defined as the ratio of amplitude of reflected wave to that of incident wave.

$R={\left(\frac{k_{2-}{k}_1}{k_2+k_1}\right)}^2$

Where, localid="1657549250276" $k_2=\sqrt{\frac{2m(E-v_0)}{{}^2}}$ and$k_1=\sqrt{\frac{2mE}{{}^2}}$

Given/known parameters

$E=5eV$ and$V0=2eV$

Solution

Substituting the values in the formula:

$R={\left(\frac{\sqrt{5-(-2)}-\sqrt{5}}{\sqrt{5-(-2)+\sqrt{5}}}\right)}^2$

$R=0.007$

Explanation and Conclusion

The reflection probability is $0.007,$i.e., there is$0.7\%$ chance of particle being reflected back.