[Kilgore Trout]

Hello, I am in the Quantum mechanics and Spectroscopy part of pchem. We were assigned this homework problem to take home and do. It begins by first stating:

Let us define a "Rydberg constant" for the particle in a one-dimensional box as RL:

RL = h/8cmL^2

c = speed of light
m is mass of electron
L is length of box.

Assume that the magnitude of the Rydberg constant for hydrogen  RH = RL where RH=109737.31534 cm^-1

A) Draw an energy diagram showing the energy levels for the quantum numbers n=1,2,3,4.

This was easy. For the Bohr model, the quantized energy (En) is proportional to 1/n^2. So, the energy gaps get smaller and smaller as you go up.

For the particle in the one dimensional box, energy is proportional to n^2, so the gaps get bigger and bigger as you go up.

B) Calculate the wave number for a transition from quantum number 1 to 2, 1 to 3, and 1 to 4 using the Bohr model.

Easy. Plug in chug formula. I used (wave number)=RH*(1/n^2 initial - 1/n^2 final)

C) Calculate the wave number for the same transitions above but using the particle in a box model.

Not sure what to use here since the problem doesn't give us the length of the box, L. Any hints?

[Kilgore Trout]

Then the problem ends by asking us what is the qualitative difference between the particle in a box and the Bohr model? Do you expect the particle in a box to be able to explain the hydrogen emission spectrum?

As I stated above E for Bohr is proportional to 1/n^2 and E for particle in box is proportional to n^2 and thus I don't expect or the particle in a box model to be able to explain the hydrogen emission spectrum.

[Corribus]

I would just express it in terms of L.  And your answer in your second post is right.  However I think the answer would be better if you went just beyond the predictions of the energy levels.  That is, why is the particle in a box model not a good model of an atom?  Think in terms of what the potential energy is for the particle in a box.