# Hydrogen Atom and an Infinte Square Well

1. May 9, 2010

### VelvetRebel

1. The problem statement, all variables and given/known data

Comparing the hydrogen atom orbitals to an infinite square well.
a.) For the hydrogen atom, what is the energy difference between the ground state and the next energy level?
b.) Now 'tune' an infinite square well holding a single electron so that it has the same energy difference between the ground state and the next energy level. What is the width, L, to make that happen?
c.) Now that you have your square well tuned to match the hydrogen atom, discuss a simple spectroscopy experiment that would easily show that the atom and the square well actually are different, despite your 'tuning' to match the first two energy levels.

2. The attempt at a solution
I got the hydrogen atom to have a 10.2 eV difference. The infinite well L value turned out to be 3.33x10^(-10) meters.
However I'm not sure how to describe the spectroscopy experiment. My only understanding of this would be as the energy levels increase in each object, they would emit a different photon and you would measure a different wavelength for each one.

2. May 10, 2010

### ehild

You are on the right track. Exiting the electron to a higher level, or ionizing the atom and the particle in the box, different photons would be emitted if the higher energy levels do not match. Show that the energy of the hydrogen and that of he square well are different at the higher levels. A simple spectroscopy experiment can be performed by a simple spectrograph which works in the visible range. You know the spectrum of hydrogen. Do you get emission lines for the square well in the visible range? at what wavelengths?