Finding Energy Level Based on Wavelength?

Question

In its ground-state, a H atom absorbs a photon of wavelength 97.20 nm. To what energy level does its electron move?

The answer is 4.


How is this value reached?

Here's what I did:

c=(freq)(wavelength), (3x10^8)/(97.20x10^-9), so freq. = 3.09x10^15 Hz.

Then I used E=hv, (6.626x10^-34)(3.09x10^15), so E = 2.05x10^-18 J(?).

Finally, I plugged it into the energy level equation: 2.05x10^-18 = -B(1/x^2 - 1/1^2), with B = 2.179x10^-18...

The answer I got was 1 - which is incorrect!

I know I made a mistake on the last part, so could anyone please clarify?

Well, I appreciate the responses, could you please explain how to get the the correct answer in the way I outlined?

Also, rhsaunder, I don't quite understand what you mean by 2.05 is not equal to 2.179, could you please elaborate? Did I use the wrong constant for B?

Nevermind, I see the arithmetic error now, thanks!

Answer 1

The error is in arithmetic in the last step. 2.05 is not equal to 2.179, and the difference gives you what you want. Otherwise, the analysis is correct, although somewhat the long way around: it is easier (as well as simpler, intuitively) to handle the energy in electron-volts, compute it directly from the wavelength with the appropriate constant, and proceed from there.

Answer 2

use E=hc/wavelength. this gives the energy provided by the light used to the electron.
now add this energy to the energy of the 1st orbit of electron of hyderogen atom(i.e 13.6 ev) to get the energy of the level to which the electron moves which is 4