- #1

Danielk010

- 34

- 4

- Homework Statement
- A free proton moves back and forth between rigid walls separated by a distance L.

If the proton is represented by a one-dimensional standing de Broglie wave with a node at each wall, show that the allowed values of the de Broglie wavelength are given by the given equation where n is a positive integer.

- Relevant Equations
- ##\lambda = \frac {2L} {n} ##

##\lambda = \sqrt { \frac {(hc)^2} {2mc^2k} } ##, where k is the kinetic energy

## (hc)^2 = 1240 (ev *nm)^2 ##

Since I know from the equation the type of particle and the distance L, I thought of equating the first relevant equation to the second equation. Since n = 1, 2, 3 ..., I thought by equating the two equations I could get k = 1, 4, 9... and have the two constants equal each other. The two constants did not equal each other, so I am a bit stuck on where to go from here or where to start. I got an equation for kinetic energy in terms of n from my previous attempt, but I don't know the quantum number, n, nor the kinetic energy, k. Thank you for any help that can provided.