Answer to Question #167705 in Quantum Mechanics for Sherine Horo

Question

A stream of electrons, each of energy 𝑬 = 𝟑𝒆𝑽 is incident on a potential of height 𝑽𝟎 = 𝟒𝒆𝑽 . The width of the barrier is 20Å. Calculate the percentage transmission of the beam through this barrier.?

Answer 1

$E=3eV$

$V_{o}=4eV$

$L=20A^o=20\times10^{-10}m$

$\alpha L=\sqrt{\dfrac{2m(V_o-E)}{\hbar}}L\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space m=9.1\times10^{-31}kg$

$\alpha L=10.23$

Transmittance, $T=16\times\dfrac{3}{4}\times(1-\dfrac{3}{4})\times e^{-2\alpha L}$

$T=3.90\times10^{-9}$