An electron in a hydrogen atom relaxes to the n = 4 level, emitting light of 114 THz. What is the value of n for the level in which the electron originated?

Question

I am halfway through, but uncertain as to how to simplify the problem to completion.

(6.63 x 10^-34 J x s)(1.14 x 10^14 s^-1)= -2/18 x 10^-18 J x [1/4^2 - 1/ninitial^2)

Thank you!

Answer 1

I think you have a typo. Isn't that 2.18E-18 and not 2/18E-18? And I don't see that h*lambda. Is that 114 THz the frequency? Surely not the wavelength. Frankly, I would use a simpler formula of
1/wavelength = R(1/n^2 - 1/n^2)
1/w = 1.09737E7(1/4^2 - 1/x^2)
I think the easy way to go after that is evaluate 1/w and that equals
1.09737E7/16 - 1.09737E7/x^2 and go from there.