## What level did electron begin? (Post module problem)

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

Jennifer1E
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### What level did electron begin? (Post module problem)

An excited hydrogen atom emits light with a frequency of 1.14 x 1014 Hz to reach the energy level n = 4. In what principle quantum level did the electron begin? I am not too sure how to approach this problem. Can I get steps on how to solve it?

Sarah_Wilen
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### Re: What level did electron begin? (Post module problem)

You know the equation for the energy produced by the electron electron "path" is $E=\frac{-hR}{n_{f}^{2}}+\frac{hR}{n_{i}^{2}}$
You also know that $E=h\nu$

We can use these two equations to solve for the final energy level. The problem tells you that the excited hydrogen atom emitted light, therefore, we know that the electron must've dropped from a higher energy level. You are finding the initial energy level and you have where the hydrogen atom ended (n=4).

Steps:
1) I began by substituting the two energy equations
2) I factored out the 'hR' and rearranged the equation so I wouldn't have to deal with the negative signs.
3) I divided Planck's constant out from both sides.
4) I also divided both sides by R to get it out of the right-hand side of the equation.
5) I rearranged the equation again so that frequency/R would be on the right-hand side subtracting from 1/16 while 1/n initial would be on the right.
6) I subtracted out the right-hand side of the equation
7) I did a few more things that are easier to explain by the picture below.
8) I got my final answer of n=6

A lot of 'I's in the steps, now it's time for YOU.

Sent from Taco Bell.
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Chem_Mod
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### Re: What level did electron begin? (Post module problem)

Hey!
For this problem this is the equation. E=-R(Z^2/nf^2)- -R(Z^2/ni^2)
We can determine E of the emitted photon with the equation E=hv
so full equation is hv=-R(Z^2/nf^2)- -R(Z^2/ni^2)
When electrons go from a higher energy state to a lower energy state, they emit photons. Your problem says that light (photons) is emitted to reach n=4. Since we know that photons are emitted when going to a lower energy state, we know that n=4 is our final n (nf) value.

They give us frequency v. R is a constant. Since it is a hydrogen atom, Z=1. h is a constant. Now we can plug in everything into the equation and solve for ni.