Electron in a box - wavelength of photon

[yango_17]

Homework Statement

a) An electron is trapped in a one-dimensional box that is 526 nm wide. Initially, it is in the n=2 energy level, but after a photon is absorbed the electron is in the n=7 energy level. What is the wavelength of absorbed photon?
b) Eventually, the electron ends up in the ground state. As it does so, one or more photons are emitted during those transitions. Find the wavelength of the least energetic and most energetic photons that might be emitted during all the possible transitions to the ground state.

Homework Equations

$E_{n}=\frac{n^{2}h^{2}}{8mL^{2}}$
$\lambda =\frac{c}{v}$
$E=hv$

The Attempt at a Solution

How I attempted to solve part a) was to find the difference in energy between the n=7 and n=2 energy levels(basically take just do $E_{7}-E_{2}$ using the first formula, and then use that energy and relate is to wavelength using the $E=hv$ and the $\lambda =\frac{c}{v}$ equations. Solving for wavelength, I obtained a value of 0.020224 m, which seems much too large. The same problem occurred when I attempted to solve part b), in which I designated the $E_{7}$ to $E_{1}$ the most energetic photon and the $E_{2}$ to $E_{1}$ the least energetic photon. Any help on this problem would be much appreciated, as its kept me tied up for quite a bit. Thanks!

 

[blue_leaf77]

I obtained a value of 0.020224 m

When you compare the length of the box with the Bohr radius, the value you got there actually makes sense - the Bohr radius is more than two orders of magnitude smaller than the box's length.

 

[DrClaude]

Your number appears correct. 526 nm is a huge box for an electron!

 

[yango_17]

Thanks!