# Energy Levels

The diagram (see attached) represents some of the energy levels for an atom of a gas.

White light passes through the gas and absorption lines are observed in the spectrum.
Which electron transition produces the absorption line corresponding to the lowest frequency;

A. E3 to E2
B. E2 to E3
C. E1 to E0
D. E0 to E1
E. E0 to E3

Had an exam today, had no idea what any of this means...I answered "A" but that was just a wild guess, any ideas?

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cepheid
Staff Emeritus
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1. Energy is conserved. Therefore, if an electron makes a transition from a higher energy level to a lower one, the energy that it loses has to go somewhere. In this case, it takes the form of an emitted photon (a particle of light) having exactly the same energy as the gap between the two levels.

2. A photon of frequency f cannot have just any energy. We know from quantum theory that the energy of a photon depends on the frequency of that photon in a very specific way. In other words, there is a relationship between the energy and the frequency of a photon that you should know.

3. Based on the relationship between photon energy and photon frequency mentioned above, you should be able to determine which of the energy level transitions would result in the lowest-frequency photon being emitted.

1. Energy is conserved. Therefore, if an electron makes a transition from a higher energy level to a lower one, the energy that it loses has to go somewhere. In this case, it takes the form of an emitted photon (a particle of light) having exactly the same energy as the gap between the two levels.

2. A photon of frequency f cannot have just any energy. We know from quantum theory that the energy of a photon depends on the frequency of that photon in a very specific way. In other words, there is a relationship between the energy and the frequency of a photon that you should know.

3. Based on the relationship between photon energy and photon frequency mentioned above, you should be able to determine which of the energy level transitions would result in the lowest-frequency photon being emitted.
Thanks mate, so, using the quantum theory, the formula E = hf could be used to find the frequency of each level change?

If so, the answer is "E" which, unfortunately, is completely different from the answer I gave in the exam :/

collinsmark
Homework Helper
Gold Member
Thanks mate, so, using the quantum theory, the formula E = hf could be used to find the frequency of each level change?

If so, the answer is "E" which, unfortunately, is completely different from the answer I gave in the exam :/
Sorry, but there is a lower-energy transition choice. (The problem statement said "lowest frequency" not lowest wavelength.)

Sorry, but there is a lower-energy transition choice. (The problem statement said "lowest frequency" not lowest wavelength.)
Thanks, here as the steps I followed;

1. Energy Change = Energy New - Energy Old
2. Energy Change = h x f (h = 6.63x10-34)

Is that right? Or I might have made a silly mistake?

collinsmark
Homework Helper
Gold Member
Thanks, here as the steps I followed;

1. Energy Change = Energy New - Energy Old
2. Energy Change = h x f (h = 6.63x10-34)

Is that right? Or I might have made a silly mistake?
That part's fine! It's just that choice 'E' is from level E0 to E3. The direction is correct -- the atom absorbs the energy of the photon, so the electron must gain energy (this is the conservation of energy part that cepheid discusses in a previous post). So the electron will transition from some lower energy state to some higher energy state. So the direction of choice 'E' is fine.

But there is(are) lower energy transition(s) than the step from E0 to E3. You need to pick the lowest energy transition (i.e. smallest change in energy) because that's the one that will absorb the lowest frequency photon.

That part's fine! It's just that choice 'E' is from level E0 to E3. The direction is correct -- the atom absorbs the energy of the photon, so the electron must gain energy (this is the conservation of energy part that cepheid discusses in a previous post). So the electron will transition from some lower energy state to some higher energy state. So the direction of choice 'E' is fine.

But there is(are) lower energy transition(s) than the step from E0 to E3. You need to pick the lowest energy transition (i.e. smallest change in energy) because that's the one that will absorb the lowest frequency photon.
Thanks again, If I am understanding correctly then the energy transition should be moving up energy level(s). And that the smallest change in energy should result in the smallest frequency - therefore the correct answer is "C"?

cepheid
Staff Emeritus
Gold Member
Thanks again, If I am understanding correctly then the energy transition should be moving up energy level(s).
EDIT: Yeah that's right. I thought a photon was being emitted, but the question is talking about a photon being absorbed which I didn't realize until now.

And that the smallest change in energy should result in the smallest frequency
Correct!

- therefore the correct answer is "C"?
Incorrect! The diagram is conveniently drawn in such a way that the vertical spacing between the levels is proportional to the energy difference between them. So all you have to do is find the smallest gap spacing...it's not even necessary to calculate the energy differences. The transition with the smallest spacing will be the energy transition that involves the smallest change in energy. EDIT: Answer choice C also has the wrong direction.

Last edited:
Incorrect! The diagram is conveniently drawn in such a way that the vertical spacing between the levels is proportional to the energy difference between them. So all you have to do is find the smallest gap spacing...it's not even necessary to calculate the energy differences. The transition with the smallest spacing will be the energy transition that involves the smallest change in energy. EDIT: Answer choice C also has the wrong direction.
1. Be moving up energy level(s)
2. Have the smallest change in energy

Thanks Again, I'll get there in the end collinsmark
Homework Helper
Gold Member
Thanks Again, I'll get there in the end There ya go. 