Problem

A positron is an antimatter version of the electr…

05:18

Problem 55 Hard Difficulty

(a) Beta decay is nuclear decay in which an electron is emitted. If the electron is given 0.750 MeV of kinetic energy, what is its velocity? (b) Comment on how the high velocity is consistent with the kinetic energy as it compares to the rest mass energy of the electron.

Answer

(a) $v=2.51 \times 10^{8} \mathrm{ms}^{-1}$
(b) The rest mass energy of the electron is very small, therefore, the velocity
shoule be very high.

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Physics 103

College Physics for AP® Courses

Chapter 28

Special Relativity

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Video Transcript

their lead. Mystic Kinetic energy is given by her ladder mystique. Kind of the energy is equal to gamma minus one times emcee sphere. The lamb is most of the materials is the speed off light and gum eyes, their latest a constant and it's equal to one divided by square root off one minus, we swear. Divided by C Square and the most of the electron M is a call to 9.11 Multiply by 10 to the power minus 21 kilogram. Can I take energy of the electron related mystic kinetic energy of electron? Uh, kinetic energy? The latter mystic is a cool too 0.0 point 750 1,000,000 electron vote. So zero point 750 in electron world. Let's go inward. This thing to Jules uh, relativistic kinetic energy is a cool too 0.750 multiplied by 10 to the power six electron world. Since Maggie equals 10 to the power six and we know that ah one electron Walt equals 1.6. Multiply by 10 to the power minus 19 guild and multiplying these numbers we get 1.20 multiplied by 10 to the power minus 13 Jules. And the speed of light C is 3.0 multiplied by 10 to the power eight. Made a per second. Well, uh, from this week, urgent. Let's say this is a cretin number one from equity number one weekend a soul for re and we is equal to see into screen route off one minus, uh, one minus one, divided by one less One place, uh, rely domestic kinetic energy letter, mystic kinetic energy divided by M C Square. And then we have square No, let's plug in the values. So vehicles 3.0 z Don't multiply by 10 to the power eight meters per second multiplied by, uh, squared fruit square rode off one minus one, divided by one plus with real animistic kinetic energy is, uh, 1.1 point 20 multiplied by 10 to the power minus 13. Jules, divided by mm His most off electron, which is a 9.11 multiplied by 10 to the power minus 31 kilogram multiplied by C square, sees speed off light and it's equal to 3.0 Multiplied by 10 to the hour eight and we have squared as well and solving. For we we get Ah, oui is equal to tree 0.0 Multiply by 10 to the power it multiply by zero point 835 This gives this 2.51 multiplied by 10 to the power eight meter for a second, all right, and we know that the rest energy electron dressed Most Energy electron is given by easy call to M C Square and Moss is 9.11 multiplied by 10 to the power minus 31 multiplied by 3.0 multiplied by 10 to the hour eight whole square. And this gives us 8.199 Multiply by 10 to the dollar minus 14 Jeweled. Well, let's, uh, convert this number into, uh, 1,000,000 electron volts. Let's divided by 1.6. Multiply by, uh, 10 to the power minus 13. Jules and bolted line eight with one 1,000,000 electron and we get zero point 0.5. Want one million? Electron walked well since the rest Most energy of the electron is very small. Therefore, been lost. He should be very high

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