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Problem 33 Medium Difficulty

What are the (a) energy, (b) magnitude of the momentum, and (c) wavelength of the photon emitted when a hydrogen atom undergoes a transition from a state with $n=3$ to a state with
$n=1 ?$

Answer

(a) 12.1 $\mathrm{cV}$
(b) $6.45 \times 10^{-27} \mathrm{kg} . \mathrm{m} / \mathrm{s}$
(c) 102 $\mathrm{nm}$

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Top Physics 103 Educators
Christina K.

Rutgers, The State University of New Jersey

Farnaz M.

Simon Fraser University

Zachary M.

Hope College

Meghan M.

McMaster University

Video Transcript

part a off the given problem. Since the energy is conserved, the energy e off a photo is given by he's equal to e I minus e f, where the eyes the initial energy off the hydrogen atom and, if it is the final energy, the electron energies given by minus 13.6 electoral votes. Divide by 10 square when any is the principal quantum number, we can write energy e will be key three minus the one is it quota minus 13 for six and a Tron won't Divided by three square uh minus minus minus 13. Pour into six hour from Walt divided by one square. This will give us a 12.1 electron world, but be off the problem. The photo on momentum is given by piece called Allergy to grind It by sea. Oh, we can write the energy. Been working electrode Walton to Jules Trolls. One electron Waldman Fiber. 1.6 old times, 10 to the power minus 19 jewels for a drone divided by three times 10 to the power eight meters per second speed of flight. This gives us 64 and 45 time stand to the power minus 27 k g meter per second, but see off the problem. Um, we can write the prevalent Linda is etc. Divided by he where we have for speed of light. And the plan constant gives us Ah 12 40. So 12. 40 electron Walter, then Amedure, divided by energy troll 400.1 of us from Walt. This will be worse. Irreverent off 1029 millimeter.

Wesleyan University
Top Physics 103 Educators
Christina K.

Rutgers, The State University of New Jersey

Farnaz M.

Simon Fraser University

Zachary M.

Hope College

Meghan M.

McMaster University