1. For Homework #3, you used the expression E = n²h²/(8ma²) to dete...

1. For Homework #3, you used the expression E = n²h²/(8ma²) to determine the energies of a particle in a box, and from this we calculated the wavelength of light needed to promote electron-sized particles from n=1 to n=2 levels in some nm-sized boxes. Derive a general expression that allows you to quickly calculate the wavelengths for any ni-->n2 transition (where ni and nz can be any integers), for any particle of mass m, and any box size a.
When the length of the box is tripled, what happens to the wavelength of a given transition such as n=2 to n=3? What happens to the wavelength if the mass of the particle is doubled?

2. Sketch contour maps for the following orbitals:
3py
3dxz
5dz2