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Problem 14 Easy Difficulty

A photon is emitted when a hydrogen atom undergoes a transition from the $n=5$ state to the $n=3$ state. Calculate (a) the wavelength, (b) the frequency, and (c) the energy (in eV) of the emitted photon.

Answer

a) 1278 $\mathrm{nm}$
b) $2.34 \times 10^{14} \mathrm{Hz}$
c) 0.97 $\mathrm{cV}$

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Top Physics 103 Educators
Elyse G.

Cornell University

Andy C.

University of Michigan - Ann Arbor

Zachary M.

Hope College

Jared E.

University of Winnipeg

Video Transcript

In this exercise, we have a hydrogen atom that transitions from the fifth. And are you leveled to the 3rd 1? And in this process, it, um, IDs a folding and we have to answer some questions about the full. In the first question question, they have to Khalkhali the wavelength of the folder. So in order to do that first, I'm going to calculate the energy of the emitted Fulton. So from conservation of energy, the energy of the focus will be the energy of the fifth energy level. Mine is the image of the third energy level, and we know that the energy of the 10th energy level of the hydrogen atom is given by minus 13.6, divided by N square electron votes. So the energy of a photon will be 13.6 times 1/3 squared, which is nine miners, one over five square, which is 25 checkroom votes. So this energy here is 0.90 seven electoral votes, okay? And from the energy we confined the the wave ling. So the energy of a photon is given by HC over London. So Lunda is H c over the interview HC struck 140 electoral votes millimeters and e is 0.97 electoral votes. So the wavelength Lunda is 1278. None of meters. Okay, this is the answer to question a in question be we have to calculate the frequency Notice that the energy of an electron of a Fulton is able to age times the frequency. So the frequency is just the energy divided by H. The energy is 0.97 electoral votes. An age is 4.14 times 10th the minus 15 lead from votes second. So the frequency is 2.34 times 10 to the 14th hurts. This here is the answer to question be and in questions. See, the exercise asks us to calculate the energy of the emitted full and well that we already have because we did that back in question. One question am sorry. And this here is the energy of 0.97 electoral votes. So I'm just gonna write it down here because I already explained, uh, where this energy comes from. It's just the conservation of energy. So the energy is 0.97 electoral votes. Okay,

Universidade de Sao Paulo
Top Physics 103 Educators
Elyse G.

Cornell University

Andy C.

University of Michigan - Ann Arbor

Zachary M.

Hope College

Jared E.

University of Winnipeg