A photon scatters in the backward direction 1f = 180°2 from a free proton that is initially at rest. What must the wavelength of the incident photon be if it is to undergo a 10.0% change in wavelength as a result of the scattering?

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Hello, fellow physicists today, we're gonna solve the following practice problem together. So first off, let's read the problem and highlight all the key pieces of information that we need to use. In order to solve this problem. A photon of light bounces back into its initial direction of motion. After colliding with an electron, the angle between the initial and final direction of the photon is 180 degrees. The wavelength of the photon increases by 5% following the scattering determine the wavelength of the incident proton. OK. So we're given some multiple choice answers and they're all in the same units of meters. Let's read them off to see what our final answer might be. A is 4.62 multiplied by 10 to the power of negative 12. B is 9.70 multiplied by 10 to the power of negative C is 5.11 multiplied by 10 to the power of negative and D is 9.70 multiplied by 10 to the power of negative 13. OK. So first off, let us recall that once scattering has occurred, the photon will undergo a change in wavelength. And that equation is written as follows, let's call it equation one. So delta lambda divided by LAMBDA is equal to P planck's constant divided by the mass of an electron multiplied by the speed of light multiplied by the wavelength of the incident proton multiplied by one minus cosine theta where theta represents the final direction of the proton. OK. So, oh and we almost forgot. So delta Lambda divided by LAMBDA is the percent change in the photons wavelength. So since this is the percent change in the photons wavelength, and that's given to us as 5% but we need to take five and divide it by 100 to get it into a decimal value. So when we do that, we should get 0. 50. OK. So now we need to rearrange equation one to solve for Lambda. So when we do that, we get that lambda is equal to plunks constant multiplied by one minus cosine theta divided by the mass of an electron multiplied by the speed of light multiplied by the change in the photons wavelength. OK. So let's plug in over known variables to sulfur the wavelength lambda. So the numerical value for Planck's constant is 6.63 multiplied by 10 to the power of negative jewels multiplied by seconds multiplied by one minus the cosine of 180 degrees as given to us in the problem, divided by everything divided by the mass of an electron which the numerical value for that is 9.109 multiplied by 10 to the power of negative kg multiplied by the speed of light which is 3.0 multiplied by 10 to the power of 8 m per second multiplied by the change in the photons wavelength which is 0.050. OK. So when we plug that into a calculator, we should get that. Lambda is equal to 9. multiplied by 10 to the power of negative 11 m. And that is our final answer. Hooray, we did it. So that means looking at our final answers from the multiple choice to pick from or among multiple choices, the correct answer has to be B 9. multiplied by 10 to the power of negative 11 m. Thank you so much for watching. Hopefully that helped and I can't wait to see you in the next video. Bye.

A photon scatters in the backward direction 1f = 180°2 from a free proton that is initially at rest. What must the wavelength of the incident photon be if it is to undergo a 10.0% change in wavelength as a result of the scattering?

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Key Concepts

Photon Scattering

Compton Wavelength Shift

Wavelength Change Calculation