# Early Quantum Mechanics

## Homework Statement

The hydrogen spectrum contains a blue line with a wavelength of 434 nm. Photons of blue light are emitted when hydrogen's electron drops from the fifth energy level to a lower energy level. What is the lower energy level?

## Homework Equations

1/lambda = R[1/m e2 - 1/n e2]

## The Attempt at a Solution

1/4.34 x 10 e-7 m = 1.097 x 10 e7 m e-1 [1/m e2 - 1/5 e2]
1/4.34 x 10 e-7 m [1/m e2 - 1/25] = 1/1.097 x 10 e7 m
1/[1/m e2 - 1/25] = 4.34 x 10 e-7m/1.097 x 10 e7
1/m e2 - 1/25 = 1.097 x 10 e7/4.34 x 10 e-7 + 1/25
n e2 = 4.34 x 10 e-7/1.097 x 10 e7 + 25/1
=3.96 x 10 e-14 + 25
=25
n = 5

Grrrrr! I keep getting n = 5 and I don't know what I'm doing wrong. Can anybody please help me?

Chi Meson
Homework Helper
here, the "m" is the shell number you want, and the "n" is the shell it came from, in this case 5.

Edit: No, that's what you did. Um...

When you write out "1/m e2" do you mean "1/m^2"? No...

Your math is difficult to follow. I'm thinking you are making the algebra harder than it needs to be. Your formula is correct and you should get the right results; the problem here is algebra.

Try solving the problem without cramming in all the numbers first.

ARe you required to work out the math for this? Does the fact that this photon is visible provide enough info?

Last edited:
I did mean 1/m e1 = 1/m^2

I guess my algebra is off but I've tried it several times and each time I keep getting 5. Do you have any suggestions?

Chi Meson
Homework Helper
In what you wrote, your second line is all wrong.

Again, work out the algebraic manipulation using the variables, not the numbers, it's less confusing.

Aaaaah, I got it now. Thanks Chi!!!!

Chi Meson