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A plutonium atom with a mass of $4.05 \times 10^{-25} \mathrm{kg}$ emits agamma photon with a wavelength of 0.0282 $\mathrm{nm}$ from its nucleus.What is the recoil speed of the atom after emitting the photon?

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Physics 103

Chapter 30

Quantum Physics

Cornell University

Hope College

University of Sheffield

McMaster University

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most of you don'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'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's divided by lender minus I'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'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's solve for we, um recalls Let's see, divided by re equals Etch see divided by ah screen Rudolph and not square C Square, Lambda Square Less at square. Let'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'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'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'll meter for a second.

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