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Problem 13 Easy Difficulty

A hydrogen atom is in the ground state. It absorbs energy and makes a transition to the n 3 excited state. The atom returns to the ground state by emitting two photons. What are their wavelengths?

Answer

$6.56 \times 10^{-7} \mathrm{m}$ and $\left[1.22 \times 10^{-7} \mathrm{m}\right]$

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Top Physics 103 Educators
Elyse G.

Cornell University

Marshall S.

University of Washington

Farnaz M.

Simon Fraser University

Zachary M.

Hope College

Video Transcript

Okay, so and this probably have these autumn, which is in the seconds excited state, which is an ICO street. And he goes back to the ground state, which is an echo swon. But when he passes by when he goes to an equals one, he best is fruit into an equals True. And when he goes from tree for too, he meets a photo with Waveland, loved that one. Then when he goes from true to one, he meets a second photo with Waveland Lumber two, uh and we know that's we just need to use the equation that relates energy with the Waveland between his estates, which is going to me. Let's see, one divided by I'm the one is the first photo is just 1.0 97 times into this seven four hydrogen atom. The multiplies Z square, which is one for hydrogen multiplies difference between the quantum numbers just going to be one divided by true square miners, one divided by three square. So calculating this we have on answer off one point 5 to 4 times 10 to the six. It should be a six. Therefore, we can say that the Waveland off the first forthem. It should be six point 56 times 10 to the miners, seven meters and doing the sin calculation for the second forthem we have, let's see one divided by limb. That too, because 1.0 97 times 10 to the seven emotive place Z square multiplies one divided by one miners, one divided by to square. So this gives us eight point 22 eight times 10 to this six. So the second Waveland Lambda too, is just one point 22 times two to the minor seventh meters. And that's the final answer. Thanks for watching.

Top Physics 103 Educators
Elyse G.

Cornell University

Marshall S.

University of Washington

Farnaz M.

Simon Fraser University

Zachary M.

Hope College