Is the wavelength of light emitted when the electron drops from n 3 to n/2 is shorter than the wavelength of light emitted if the electron falls from n 3 to n 1?

true and false about the excited states of electrons

[Feb. 27th, 2008|10:42 pm]

Chemistry Help

chemistryhelp
[wolodymyr]

This is the question:An electron is excited from the n=1 ground state to the n=3 state in a hydrogen atom. Which of the following statements are true (check all that apply).__ a) The wavelength of light emitted when the electron returns to the ground state from n=3 will be the same as the wavelength of light absorbed to go from n=1 to n=3.__ b)The wavelength of light emitted if the electron drops from n=3 to n=2 will be shorter than the wavelength of light emitted if the electron falls from n=3 to n=1.__ c)The electron is further from the nucleus on average in the n=3 state than in the n=1 state.__ d)It takes more energy to ionize the electron from n=3 than from the ground state.__ e)For n=3 the electron is in the first excited state.So, first chose c) and b) because, I admit, I misread b). Then I realized that b) is false - if the electron travels a shorter distance it will release LESS energy and thus a LONGER wavelength of light. So I entered just c), and I was wrong a second time, and...now I'm down to my last submission.From what I understand, a) is false because the electron won't necessarily go back down to n=3 in the same single jump that took it there. b) is false for reasons given above. d) is false because the further the electron is from the nucleus, the easier it will be to ionize. e) is wrong because the first excited state is n=2.Is there something I'm missing? I would be, as ever, grateful for your help in understanding this.

thanks!

Comments:

From:

blueskypenguin
2008-02-28 11:23 am (UTC)

My first instinct was a), and since you've ruled out the others so certainly, I'd go for that. Sorry, quantum theory isn't my strong point.

From: wolodymyr
2008-02-28 08:31 pm (UTC)

You are right, simplicity wins, and thank you for that icon.

From: a_pawson
2008-02-28 12:10 pm (UTC)

I would say a) and c) are true.a) is true as it is simple application of the equation E=hc/λ The electron may fall back to ground state via n=2, but you cannot assume that and have been given no information to suggest it will happen by that mechanism.b) is false, the wavelength would be longer. Again it is simple application of the same equationc) is true since the electron has been moved to a higher orbitald) is false as the electron is now further from the nucleus, the force of electrostatic attraction is lower

e) is false since there us a level n=2 between n=3 and the ground state

From: uberjason
2008-02-28 04:06 pm (UTC)

Your problem with (a) was that it wouldn't necessarily go from n=3 back to n=1 directly. This is a reasonable concern, but I think (a) was trying to imply that it would simply go from n=3 back to n=1 directly. Given this, you can take (a) as true.

From: wolodymyr
2008-02-28 08:10 pm (UTC)

It is true, and I was reading too much in. Dude, it's just, we spent one third of class talking about the ain't-necessarily-so-ness of A!

Thanks for helping me return to more casual and multiple-choice-friendly reason.

From: invaderxan
2008-02-28 11:44 pm (UTC)

There isn't technically enough information to say if a is true. If you assume that the electron jumps directly between n=1 and n=3 (for example, if the transition to n=2 is forbidden), then it is true.

Just FYI, where the emitted photons are the same frequency as those absorbed like this, it's known as 'resonance fluorescence'...