Energy Level question (quantam physics)

[quickslant]

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 engery level to a lower energy level. What is the lower energy level?
Given
Wavelength = 434 nm
n1 = 5
n2 = ?
R = 1.097 x 10^7 m^-1 (which i am not sure what this means or how to apply it but anyways)

Homework Equations

1/wavelength = R [ 1/n2^2 - 1/n1^2]

The Attempt at a Solution

1/434 = (1.097 x 10^7 m^-1) [1/n2^2 - 1/5^2]
1/434 = (1.097 x 10^7 m^-1) [1/n2^2 - 1/25]
0.0023 = (1.097 x 10^7 m^-1) [1/n2^2 - 0.04]
0.0023 / (1.097 x 10^7 m^-1) = [1/n2^2 - 0.04]
((0.0023 / (1.097 x 10^7 m^-1)) +0.04 = 1/n2^2

AND now I am totally lost because it doesn't make any sense.. plug those values into your calculator and i get the exaxt same number for n2 as i started with n1 jeez! SOMEONE HELP!

 

[Kurdt]

R is Rydbergs constant. You need to rearrange the equation you provided for n₂.

Remember that is 434nm aswell.

 

[quickslant]

does nm = Nanometers?

 

[Kurdt]

Yes. 1nm = 1x10^-9m