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Problem 37 Medium Difficulty

(II) A gamma-ray photon produces an electron and a positron, each with a kinetic energy of 285 keV. Determine the energy and wavelength of the photon.

Answer

$1.592 \mathrm{MeV}$ $7.81 \times 10^{-13} \mathrm{m}$

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Video Transcript

Hello, Strains. Let's start our discussion. Their production. What is spare production? If Ah B'more Photo on strikes with a heavy maker than it will produce an electron and a positron. This electron Aryan was drawn in. Combined form is called a pair. That's why it's colder air production. Now suppose the kinetic energy off this electron and positron is toe 85 kilo electric mold where defied like prom. For now, we have to find out that energy off for tone and a Vaillant off this for Tony. Okay, very simple. This energy off four tone is converted into energy and zero for Elektrim and inner zero positron. Okay, this will for the right, as Rashed must energy off Electron plus Kaine Antic energy off electron plus rash mercenaries. You've positron plus kinetic energy off positron. Now this rest mass energy off electron and this rest mass energy off posit Rome is 0.51 Mag electoral gino 0.5 on mega electron work. Let's 0.51 mag electron world now the kind Knittig energy off electron positron is given us 25 low electron world. So it will be to 85 kilo electron world last were to five kilo electoral word. So it will comes to obey 1.2 Mega Electron ward plus 5 70 kilo electrical. If I can work this in Killer Electron Wharton Mag Electron world and it will comes to be a 700.57 Jiro, if I can work this glow electoral wards in mag electron work than it will comes Toby 0.57 Jiro Mag Electric word ny I can add them. Okay, so if I will add them, then it will comes to be 1.59 Mega electrical. Here is the energy or photo. Now the energy off the four tone comes to be 1.59 mega like tone Ford. Now, if I have to find out the violent off this four tone, then I would like at sea by Lambda. This is a frequency it Ganga Newton s C By lambda. It will be 159 mag electrical. I have approximately this product off playing constant speed. Off light will be 140. Electron ward Nano meter upon Lambda by 1.59 into 10 days past six. Electrical from here. Electron Morton direct inward will cancel out. So the value of Lambda comes Toby. 1240 by 1.59 Okay, uh, nanometer in cooked. And this by six. This is the nanometer. It will be return extenders by minus nine meter. Then just six. Uh, I d white this, then it will comes to be 7 79.877 79 Born age seven in tow. 10 days by minus 15. Major, this is stuff they've lent off this 14. Well, this is all from before this, will you? I hope you will like the video. Thank

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