a-blue-green-photon-lambda486-mathrmnm-is-absorbed-by-a-free-hydrogen-atom-initially-at-rest-what-is

Question

A blue-green photon $(\lambda=486 \mathrm{nm})$ is absorbed by a free hydrogen atom, initially at rest. What is the recoil speed of the hydrogen
atom after absorbing the photon?

Zulfiqar Ali · Accepted Answer

be equals m We divided by scare route off one minus we square divided by C square is the expression for the relativistic momentum off an object. Er NBC cretin uh, moss off object is M and speed off object is free. A c is the speed of light. Uh, not applying conservation of momentum. Uh, initial momentum equals final momentum. An initial momentum is ah, the some off momentum off hydrogen and a momentum off put on their four p. Initial equals momentum. Uh, five region hydrogen in issue. Bless momentum or foot on mo mentum or foot on initial. And this initial momentum is equal to final momentum. Ah, mo mentum Final Momenta move by Christian Ah, Final momentum of hydrogen Less final momentum or for dawn final Momenta Mall. What on here? Um, hydrogen atom is initially a crest. Came for, um, initial momentum off hydrogen atom. Ah, zero therefore Ah, here he is. Zero. You in issue be initial for hydrogen equals zero. And the final moment, um, off the photons is zero is It is embedded in the hydrogen atom. Therefore final momentum put on Ah, final momentum off foot on final equals zero and Therefore, we have, um mo mentum. Initial momentum off tone in issue momentum off. Put on equals. Um, final Momenta More fight region. Final momentum off. Ah, hydrogen, hydrogen and final momento. And further well went off. Uh, lesser eyes given in nanometers. Let&#x27;s convert it into meters. So Lamda equals lambda babble and off the laser equals for And the six nanometers for 86 nanometers 4 86 nanometers equals four. It is six. Multiply by 10 to the power minus nine meters. And the expression for the Momenta move for Tony is given by, uh, being for tone. A momentum off for tone in issue is equal to etch divided by lambda and and here, uh, momentum off hydrogen. Um, minimal hydrogen final equals and not be. I am not re divided by, um, straight route off one minus. We squared, divided by C square Here. The wrist muscle hydrogen atom is I&#x27;m not and tow Calculate the record speed off the hydrogen atom. Let&#x27;s create initial momentum off tone and final moment to move hydrogenated. Um, is we know that our initial momentum off put on initial momentum off for tone equals ah, final Momenta Mawf hydrogen, hydrogen, atom, hydrogen eight on Let&#x27;s plug in the values Reno date Initial momentum overtone is h divided by lambda equals. Uh uh Then finally Momenta more hydrogenated recalls and not we divided by under route off one minus we squared, divided by C square. Now screening on both sides. Let&#x27;s do squaring on both sides. We have HD mighty by lander hold scare equals I am not. We hold scare divided by, um one minus We squared divided by sees where and for dinner we have one minus we squared, divided by C square times each divided by lambda Whole sphere equals and not we hold square And finally we have relation for velocity we and re equals Sometimes it seems the speed of light in eighties blanks constant C times each divided by ah, square root off scared Rudolph I am not square and not square landed square Ah C square minus eight square No, let&#x27;s plug in the values, uh, we equals be equals pre Multiply by 10 to the power eight into 6.63 multiplied by 10 to the power minus 34. Divided by divided buying. Uh, spare Rudolph scared Rudolph 1.6741 point 674 Multiply by 10 to the power minus 27. Hold skater into for 86 month supply by for 86 multiplied by 10 to the power minus mine all square into three. Multiply by 10 to the power eight old spare minus six point 63 Multiply by 10 to the power minus 34 whole square minus 34 whole square and therefore re equals zero point 816 meter per second. So the record speed of the hydrogen atom after it zapping the photon is 0.816 meters per second.

Zulfiqar Ali · Answer

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&#x27;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&#x27;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&#x27;m not square land a square divided by it&#x27;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&#x27;m not square Lambda Square divided by it&#x27;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&#x27;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.

Zulfiqar Ali · Answer

most of you don&#x27;t him, Adam? Uh, M equals 4.54 point 05 multiplied by 10 to the power minus 25 minus 25. 25 kilograms. Uh, the moss off plutonium and we blend off Gamma foot on Lambda equals ah, 0.2 It do nanometers. And it&#x27;s equal to 0.282 multiplied by 10 to the power minus nine meters. And we need to find out record speed off the off, Dad going Speed! Recoil. Speed off the plutonium. Adam! All right, Well, uh, applying conservation of momentum. We have Ah, we have zero equals. It&#x27;s divided by lender minus I&#x27;m not. We are divided by a squared Ruto one minus. We square divided by C square. Since momentum is conserved, Therefore, we have zero equals this divided by lambda minus I&#x27;m not to be divided by square root of one minus were scared about a C square. Further, we have h divided by lambda equals, but I am not re divided by square root off one minus We squared, divided by C square. Let&#x27;s solve for we, um recalls Let&#x27;s see, divided by re equals Etch see divided by ah screen Rudolph and not square C Square, Lambda Square Less at square. Let&#x27;s plug in. The values be equals edges 6163 Multiply by 10 to the power minus 34. Multiply. They see speed of light. Three. Multiply. We tend to the power it divided by divided by a squared. Oh, um, and not scared him not. He&#x27;s a 4.5 multiplied by 10 Judy Bonner, minus 25 full square multiply by three. Multiply by 10 to the power age four square Multiply by land days 0.0 282 Multiply by 10 to the power minus line. Uh, 10 to the dollar minus nine plus ex script playing constant squared is approximately zero X square. UH, 6563 Multiply 10 to the power minus 34 square. So it&#x27;s a very small number. Therefore, it cycled approximately equal to zero and solving this We have vehicles 19.89 divided by, um square root off, um 1173 point 95 Multiply by 10 to the power minus four and B equals 19.19 point 89 divided by, uh 0.34260 point 34 to 6 and this gives this are 58.0 meter per 2nd 58 points it&#x27;ll meter for a second.

Zachary Warner · Answer

for part A were asked to find the wavelength lambda of a hydrogen atom going from the initial state of four to the in final state of to the equation that governs this wavelength is one over. Lambda is equal to the Ripper. Constant times one over incidents squared, minus one over and spice squared. So in other words, Lambda is just going to be the inversion of what&#x27;s on the right side of the equation. So we&#x27;re just going to raise both sides of the equation to the minus one to get Lamba. So we have our sub age times one over in final square, minus one over an initial squared. This all gets raised to the negative one. So playing in the values for the Rittenberg Constant, which is 1.97 times 10 to the minus seven, and the values for the final and initial states of the orbital, we find that lambda is equal to 486 times 10 to the minus nine meters or 486 nano meters. You could write it either way, but I&#x27;m gonna write it as nano meters. Linkenbach said. It is the solution for part a part B wants us to find the speed of the Adam. The recoil speed is gonna be equal to place Constant divided by the massively Adam times, the wavelength and of course, wavelength. We&#x27;re gonna use units of meters. So it&#x27;s 486 10 10 minus nine meters. Plank&#x27;s constant is 6.626 times 10 to the minus 34 jewell seconds. And then in here is the mass of the hydrogen atoms 1.67 times 10 to the minus 27 Plugging these values and we find that the speed V is equal to zero 0.815 meters per second American box. That is our solution for part B.

Zulfiqar Ali · Answer

Let&#x27;s sold Barty. First of all, let me a picture of this problem. We have a foot on. Ah, let&#x27;s say this is the foot on having babbling Lambda and its initial momentum. I&#x27;ll be I b B for foot on initial momentum of put on equals edge divided by lender. And then we have a hydrogen atom. Hydrogen hydrogen is initially at rest did for Ah, it&#x27;s a momentum before Colijn is zero. So initial momentum the I initial momentum of hydrogen is equal to zero. Optical legion Hydrogen atom emits an identical foot on perpendicular where Ben Dickler to the direction off, Uh, the foot on before collision. So this is the foot on after collision and after college in its final moment. Um, B yeah. Final momentum of foot on equals edge divided by lender. Since this photo on a collision after foot on after collision is identical to the put on before college in there for its momentum is the same, but it&#x27;s in a different direction. It is perpendicular to the original direction off put on and this hydrogen Adam records, huh uh, in the opposite direction, in the hope of the direction and did it for final Momenta. Move. Hydrogen is given by I am not times we divided by square root off one minus the square one minus Reece squared, divided by C square. So this is the final momentum off. Ah, I did in Adam. No, let me draw directions. Uh, this is ex direction. And this is why direction before call it in on the total momentum alone. Why exists alone? Why exists Equals zero. So momentum along why exes equals, uh, zero before collision. And therefore according to conservation of momentum, um, daughter, momentum along, uh, why exes be prime wide. Let&#x27;s see should also be equal to Zito. This is what conservation of momentum stays. And therefore we have a itch divided by lender, which is the momentum of limited foot on we hided hydrogen Adam equals and not dimes. We divided by ah, square root off one minus. We square divided by C square. So this equation comes by using conservation off uh, Mento, no screaming on both sides. We have it&#x27;s square divided by Linda Square equals I am not screen times. Um we get square. We h is the velocity of hydrogen Adam after collision divided by one minus. Uh, we each square divided by C squared in this equation we need to find out we lost your find Richard and solving Ah, we edge comes out to be We lost your hydrogen after religion is equal to it&#x27;s time See, divided by square root off I&#x27;m not square I&#x27;m not square c square land a square less and swim. Now let&#x27;s plug in the values We have blanks constantly. 6.63 multiplied by 10 to the power of minus 34 Jule second, multiply very sees the speed of light free Multiply by 10 to the power eight liter per second divided by then we have square groot off. Um I&#x27;m not I&#x27;m not. Is 1.674 multiplied by 10 to the power minus 27 old square into a tree Multiply by 10 to the power it call it square Multiply by and lender in this case is ah 102.6 Nana meters. Now which 102 point six multiplied by 10 to the power minus nine square. Bless on Then we have blanks constant 6.63 multiply by tend to devour minus 34 whole square. Okay, so solving this, we have we etch just velocity of hydrogen Tatum Article Legion equals 19 going to 89 divided by, uh, squared Ruutel Square Rudolph 27 0.72 Bless, uh, 27 points even to bless. 43 point 43 point mine six Multiply by 10 to the dollar mind 16 and excuses 3.78 Meet her for a second. So this is the velocity of fire originated after collegian? No, let&#x27;s hold part B. So in bar being the foot on after collision moves in the opposite direction to the original proton. Uh, let&#x27;s see you see the foot on, um, and after collision with hydrogen atom for dawn moves in the opposite direction in the second case in the opposite direction. So hair momentum for dawn is B equals itch divided by Linda. Initially, hydrogen is a crest. Therefore, its initial momentum B i h equals zero and initial momentum off tone is given by h divided by Langer. Uh, this is before before religion and after a collision. The moment of a photon is in the opposite direction and it&#x27;s equal to each other. So final momentum or foot on equals? Uh, h divided by lambda. It&#x27;s divided by Landa on dhe. Then we have ah, momentum off hydrogen atom. Uh, final human to move Hydrogen equals, Uh, I&#x27;m also a hydrogen atom. Um, most of fighters in Adam Multiply Baby lost you if I didn&#x27;t. Adam divided by, uh, square root off one minus. We squared, divided by Caesar when an image is actually the rest Muscle hydrogen Adam No, Again, a blind conservation off, uh, momentum. We have each divided by lender. It&#x27;s divided by lambda equals minus. It&#x27;s divided by Landa unless marceau fight region times we lost your hydrogen divided by a squared Ruto one minus b squared, divided by C square and solving for we We have lost your fighters and Adam is equal to two times Blame Constant time Speed of light divided by scared bruto muscle If I didn&#x27;t Adams creator uh, multiply bread landed square multiply by a C square less four times it&#x27;s square and leading the values we lost your fight with an animal equals, uh to multiply by 6.63 multiplied by 10 to the power minus 34 multiply by three multiply by 10 to the hour. Eight meters per second speed of light divided by, uh, Then we have, uh, muscle. Hydrogen. So square root off home 1.674 1.674 multiplied by 10 to the dollar minus 24 whole square Multiply by lambda is 10 to 1 to 2.9. Multiply by 10 to the dollar, minus nine Whole square Multiply by So let&#x27;s do it here. Multiply by tree, multiply by 10 to the power it full square and then bless for its square is approximately zero. So the whole expression comes under the square root and solving. We have, uh, lost your fibers and Adam equals, uh, 39.7, 39.7, divided by 5.26 which gives us 7.5 five meter for a second

Sanjeev Kumar · Answer

from skittling. You know, the whole novel, you know, does Linda Burnett a London Underbrush manis? I&#x27;m going to London to one now. Yes, we know that that is a closed toe e dish. And from here we can find the in dash u minus. Hence we can write at the lander dash. That&#x27;s the upon lender Martinus. And these would no people plugging all the decorations for getting the ready off Lambda that is six foreign six into tunnels to Poland, minus 34 guarded by Linda 7.5 into 10. Dunstable minus 90. The little 17 fights. But And this is my reply with being in tow, generous to poverty minus one by two into 19.1 into turn this to go minus multiply with 1.5 into trendiest people for it. You&#x27;re reading the value of flounder dash That doesn&#x27;t quotes to. I just hate perform. 2.6 into generals took over minus 16. Here we get you, Linda. That did the work, you know, under dash kind of send off. Not suitable to 5.839 into tennis to perform almost World reader. Yes, I do now in part we have. We know that you don&#x27;t remember the vegetables you number Dish my number Learning from here in part in you can find, you know that today&#x27;s was true course and worst one minus their delenda, Linda&#x27;s No. One in worst plywood. There&#x27;s a send off by 28 into tenders for four months. Well divided when I want it divided 6.6262 genders over minus 34. This is the light by 9.1 into underscore minus 34. Multiple with you tonight he had regained their Brendan, don&#x27;t you think once you find one.

Problem

A hydrogen atom, initially at rest, absorbs an ul…

Problem 43 Hard Difficulty

A blue-green photon $(\lambda=486 \mathrm{nm})$ is absorbed by a free hydrogen atom, initially at rest. What is the recoil speed of the hydrogen
atom after absorbing the photon?

Answer

0.816 $\mathrm{m} / \mathrm{s}$

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