## Rydberg Formula

H-Atom ($E_{n}=-\frac{hR}{n^{2}}$)

clairehathaway 2J
Posts: 102
Joined: Wed Sep 30, 2020 9:38 pm

### Rydberg Formula

I was trying to calculate the energy of light absorbed from an electron (in a hydrogen atom) going from n=2 to n=4.
In order to solve it I used the equation $E_{n} = -\frac{hR}{n^{2}}$ and plugged in n=2 and then n=4 and then used plugged those results into the deltaE = Efinal - Einitial (deltaE = E(4) - E(2)). When I did that I did not get the right answer so then I tried using the Rydberg equation with n1=4 and n2=2 ($v = R(\frac{1}{n_{1}^{2}} -\frac{1}{n_{2}^{2}})$) and then used plugged the answer I got from that into E=hv, and that gave me the right answer.
I thought that either way would give you the same answer because I thought that $E_{n} = -\frac{hR}{n^{2}}$ would give me the energy at certain n levels and then I could subtract them to get the amount absorbed. Why doesn't that equation work but the Rydberg equation does?

Kailani_Dial_2K
Posts: 170
Joined: Wed Sep 30, 2020 9:44 pm
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### Re: Rydberg Formula

So did you do final minus initial? You should have plugged in n=4 first and then subtracted n=2 from that value as n=2 is your final value. I would try this and then check your answer again. The equations should give you the same outcome as one is derived from the other.

(-hR/16) - (-hR/4) should give you the energy of the electron.

From the energy of the electron you have to find the energy of the photon by multiplying your answer by -1.

You know have the energy of the Photon so you should then use E=hv and that should give you the right answer. I hope this helps

Astha Sahoo 3I
Posts: 95
Joined: Wed Sep 30, 2020 9:52 pm
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### Re: Rydberg Formula

I agree with what was said above! Also make sure you have all the signs(+/-) the right way since that messed me up the first couple of times I did the problem.

Jason_Glass_2L
Posts: 92
Joined: Wed Sep 30, 2020 9:43 pm

### Re: Rydberg Formula

To add on, I realized you said that you plugged in n=4 into n1 and n=2 into n2. Just remember for the Rydberg equation if the negative isn't factored out with the R constant in the equation, the n that comes first in the equation will be your starting n level and the n that comes second in the equation will be your final n level.