Question

If a beam of electrons impinges on an energy barrier of height 0.03 eV and of infinite width. Find the fraction of electrons reflected and transmitted at the barrier if the impinging electrons
are having energy 0.04 eV.

Answer 1

The transmission coefficient for the step-like potential 

$$T=\frac{4\sqrt{E}\sqrt{E-V_0}}{(\sqrt{E}+\sqrt{E-V_0})^2}$$

$$=\frac{4\sqrt{0.04}\sqrt{0.04-0.03}}{(\sqrt{0.04}+\sqrt{0.04-0.03})^2}=0.889$$

The reflection coefficient

$$R=1-T=1-0.889=0.111$$