Physical Chemistry: Quantum Mechanics

Question

An electron at energy level 5.0eV approaches a step potential of height 2.0eV. What are the probabilities that the electron will be reflected and transmitted?

Answer 1

Try this site.

quantummechanics.ucsd.edu/ph130a/130_notes/node149.html

P_refllection = [(k-k')/(k+k')]²

for x<0, k =[(8mE(π²/h²)]^1/2

and x>0 k' =[(8m(E-V_o)(π²/h²)]^1/2

E = 5 eV

V_o = 2 eV

P_refllection = [(k-k')/(k+k')]² = [(5^1/2-(5-2)^1/2)/(5^1/2+(5-2)^1/2]² = (5^1/2-3^1/2)²/(5^1/2+3^1/2)²= (0.254/15.7) = 1.6%

P_transmission = 100%-1.6% = 98.4%