What is the Angle of Refraction for Electrons in a Metal Surface?

[kasse]

Homework Statement

When an electron beam is incident on a metal surface at an angle tetha 1 to the normal, electron waves are refracted into the metal at an angle tetha 2, following Snell's law. The effect on an electron can be represented approximately by a drop in its potential energy.

For a particular metal surface, the size of this drop is 1.9E-18 J. If the energy of the incident electron beam is 1.6E-18 J, and its angle of incidence on the surface is 45 degrees, calculate the wavelengths of the electron waves inside and outside the metal and hence the angle of refraction of the electrons in the metal.

2. The attempt at a solution

E = 1.6E-18 = hf1 --> f1 = 2.42E15 Hz.

E = (1/2)mv1^2 = hf1 --> v = 1.87E6 m/s

lambda 1 = 1.87E6/2.41E15 = 7.8E-10 m

If the energy drop is bigger than the initial energy, the energy in the metal will be negative, and hence the frequency will be negative (impossible!), and I won't be able to calculate lambda 2. What is wrong here?

 

[Redbelly98]

I think the energy drop refers to potential energy. Perhaps classical conservation-of-energy methods can be used.

 

[dlgoff]

"If the energy drop is bigger than the initial energy, the energy in the metal will be negative, and hence the frequency will be negative (impossible!),..."
I agree. Are you sure the incident energy is 1.6E-18 J?