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Problem 21 Medium Difficulty

A photon produces a proton-antiproton pair according to the reaction $\gamma \rightarrow \mathrm{p}+\overline{\mathrm{p}} .$ What is the minimum possible frequency of the photon? What is its wavelength?

Answer

$f = 4.53 \times 10^{23} \text{Hz}, \lambda = 6.62 \times 10^{-16} m$

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Video Transcript

in this question. We're looking at the production off a photo on producing a pair off. Put on an anti proton, not find what is the minimum frequency. We need to first understand the frequency is involved in the energy off the off the photo. Right, Because energy of photons is given s hitch F thanks. So e e is proportional to f So a high frequency will give would mean that the photo on s higher energy. So what we're actually looking for is a key West the minimum energy required by the photon in order for this reaction to take place. And that would be by assuming de T products come out without any kinetic energy. So they come out and they are being produced while being at rest. And this would give us the minimum possible energy that's required. And they were just BD rest mess energies off our final products. And so the rest miss energy we can't find by getting equals two empty square. Thanks, Andy. And that she would be the mass off the protons, right? Multiplied by C square. The rest energy of proton is secure given to be, uh, night treat eight point tree MTV. All right, but since we have to off this protons so it got much played it by two. So this is the energy off our photon. And so our frequency given us the over spa. Sorry. Each you hear, Hohst. Thanks. Constant. 6.626 Time stand part minus 34. Putting into calculator. We should get 4.5 4.5 tree constant politan tree nuts. Now take note. 30. Energy over here. You will need to convert to s I units. All right. You know, there's good s i units for frequency, so we gotta multiply a further by 1.6 times sent Po minus 19. Sorry. Minus 13 juice per m E v Not to convert to juice, which is as our units before he can get this final answer in terms off s I units, you re fling. We know it's related to the speech over the frequency. All right. Said we already have two frequency, so we just have to substitute value in my speed off light, but about 4.5 tree time to send part a tree and we should get 6.62 times 10 Paul minus 16 meters. So this is d we fling for flight

National University of Singapore
Top Physics 103 Educators
Elyse G.

Cornell University

Andy C.

University of Michigan - Ann Arbor

Zachary M.

Hope College

Meghan M.

McMaster University