# Infinitel potential well

1. Jun 8, 2014

### Meekay

three parts to this one, I cant seem to justify my values, units cancel, but the numbers don't seem right. I think I may have used a wrong equation for part B but I don't know what else to use.

Problem: An electron is confined to an infinitely deep potential well of width 0.120 nm.
a.) Calculate its ground state energy, E1
b.)If the electron makes a transition from the n=3 state to the n=2 state, how much energy is carried away by the emitted photon?
c.)What is the wavelength of this photon?

equations:

a.) $$E_1 = \frac{pi^2 (hbar c)^2}{2M_e C^2 a^2}$$

b.) $$E_\gamma = E_3 - E_2$$

c.) $$\lambda = \frac{hc}{E_\lambda}$$

My attempt:

a.) using hbar*c = 197 ev*nm and MeC^2 = 511000 ev i get a value of 26.02ev for E1

b.) using the same equation as above for the n=3 and n=2 states and subtracting I get 130.13ev

c.) using hc = 1240 ev*nm I get an answer of 9.53 nm which doesn't seem right to me. I feel like the photon should have a larger wavelength.

2. Jun 8, 2014

### Simon Bridge

Why do you think the photon should have a bigger wavelength?

Lets see - using $h= 2\pi \hbar$ ;$$E_n=\frac{n^2(h c)^2}{8mc^2a^2}=n^2E_1$$ (when you use LaTeX, put a backslash in front of the symbol name so \hbar renders as $\hbar$ etc.)

hc=1239.8 eV.nm
mc^2=511000 eV
a=0.120nm

Looks good to me:
Go through the arithmetic one step at a time, make sure you have squared the correct terms.