According to the quantum-mechanical model for the hydrogen atom, which of the following electron transitions would produce light with the longer wavelength:

Question

2p --> 1s
or
3p --> 1s

I have the answer, which is 2p --> 1s, but can someone offer some help as to how this is determined?

Thanks for any help.

Answer 1

Make a diagram of the orbitals like so. You need to draw it out on a sheet of paper because I can't do it on the board.

-----------3p

-----------2p

------------1s
Now draw lines from 3p to 1s and from 2p to 1s. The most energy is emitted when the electron falls the most distance and the least energy is emitted when the electron falls the least distance.
The formula for energy is
E = hc/wavelength.
So if you want the longer wavelength, that means the denominator is larger which makes the right side of the equation lower and that means lower energy; therefore, you want to pick the transition that gives the least energy. I hope this helps.