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A hydrogen atom, initially at rest, emits an ultraviolet photonwith a wavelength of $\lambda=122 \mathrm{nm} .$ What is the recoil speed of theatom after emitting the photon?

$=[3.25 \mathrm{m} / \mathrm{s}]$

Physics 103

Chapter 30

Quantum Physics

Rutgers, The State University of New Jersey

Simon Fraser University

Hope College

McMaster University

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prevalent off emitted ultraviolet for tone from hydrogen atom equals 122 nanometers. Um, Linda off emitted ultraviolet for tone from hydrogen atom equals 1 22 nanometers, 1 22 nanometers. Uh, equal 1 22 Most of life I 10 to the power minus mind meters. We know that momentum. All foot on B foot on Momenta. More foot on equals Etch divided by Landa hse Blank constant and lambda is the vab lint. And, uh, here a moment of a hydrogen atom. Can the returnees momentum or hydrogen atom? Mmm. Is equal to I am not. We divided by square root off one minus Lee Square divided by C square. Here I am not. Ah, eyes the rest Months of hydrogen atom and I'm not equals. I am not equals. 1.6741 point 674 Multiply by Dan to the power minus 27 Mmm. 10 to the power minus 27 kilograms And C is the speed of flight and B is the a record speed off the hydrogen atom on DDE. But equating the momentum off tone in momentum off hydrogen atom. We have momentum. Be Oh, foot on for dawn equals momentum off hydrogen Adam and putting the values momentum off. Aton is lend a H, divided by lander and momentum of hydrogen atom equals and not times we divided by square root off one minus. We squared, divided by C Square and further and not I am not times Linda divided by it's times we equals square root off one minus B squared, divided by C square. Simplifying or taking square on both sides we have I'm not square land a square divided by it's queer times. The square equals one minus. We squared, divided by sees where and, uh, further behind we square divided by C square less I'm not square Lambda Square divided by it's square times we square equals one. And, uh, finally we have re equals really equals Ah, see into see into one place and not square. C square landed square divided by eight square on. We have minus one divided by two. Find the power. Now let's plug into values. We equals three. Multiply by 10 to the power 83 Multiply by 10 to the power eight. I came to one plus 1.674 one point 674 Multiply by 10 to the power minus 27 kilograms, which is the rest myself off a proton into three. Multiply by 10 to the power eight meters per second. The speed of light into 122. Multiply by 10 to the power minus mine meters divided by divided by blank constant in playing constantly. 6.63 Multiply by stand to the power minus 34. Jule second racket close and we have minus one by two. In the experiment and solving, this weekend, we equals Ah, 3.253 point 25 meter for a second, so we have 3.25 meter for a second.

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