Step up and Step down Potentials

[hectorzer]

Homework Statement

What fraction of a beam of 8 eV electrons is reflected by a potential step up of height 6 eV? What fraction is reflected from a step down of 6eV?

Homework Equations

R=$(\frac{k_{1}-k_{2}}{k_{1}+k_{2}})^{2}$

Exchange $k_{1}$ and $k_{2}$ for the step down potential.

$k_{1}$=$\frac{\sqrt{2mE}}{h/2pi}$

$k_{2}$=$\frac{\sqrt{2m(E-U0)}}{h/2pi}$

The Attempt at a Solution

I got 1/9 for the step up.

But I got the same for the step down potential, which I don't think is right. Am I doing anything wrong for the step down potential? Or should you get the same answer for the step down as for the step up?

 

[anathema]

Thank you for your question. The fraction of electrons reflected by a potential step can be calculated using the equation R=(\frac{k_{1}-k_{2}}{k_{1}+k_{2}})^{2}, where k_{1} and k_{2} are the wavevectors of the incident and reflected electrons, respectively. For a step up potential, the reflected electrons have a higher energy than the incident electrons, so k_{2} is larger than k_{1}. This results in a smaller fraction of reflected electrons, which you correctly calculated as 1/9.

For a step down potential, the reflected electrons have a lower energy than the incident electrons, so k_{2} is smaller than k_{1}. This should result in a larger fraction of reflected electrons. To calculate this fraction, you can substitute k_{1} and k_{2} into the equation and solve for R. The result should be larger than 1/9, indicating that more electrons are reflected from a step down potential compared to a step up potential.

I hope this helps clarify your understanding of the concept. Keep up the good work in your studies!