💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

A positron is an antimatter version of the electron, having exactly the same mass. When a positron and an electron meet, they annihilate, converting all of their mass into energy. (a) Find the energy released, assuming negligible kinetic energy before the annihilation. (b) If this energy is given to a proton in the form of kinetic energy, what is velocity? (c) If this energy is given to another electron in the form of kinetic energy, what is its velocity?

(a) $1.64 \times 10^{-13} \mathrm{J},(\mathrm{b}) 1.34 \times 10^{7} \mathrm{m} / \mathrm{s},(\mathrm{c}) 2.89 \times 10^{8} \mathrm{m} / \mathrm{s}$

Physics 103

Chapter 28

Special Relativity

Relativity

Cornell University

University of Michigan - Ann Arbor

Hope College

University of Winnipeg

Lectures

02:51

In physics, wave optics is…

10:02

Interference is a phenomen…

02:21

(a) How much energy is rel…

03:45

An electron with a total e…

03:40

A muon has a rest mass ene…

04:19

03:39

An electron has a speed of…

09:05

An electron and a positron…

02:53

05:25

(a) Beta decay is nuclear …

03:44

06:46

When an electron and posit…

06:01

The rest energy of an elec…

04:22

07:43

01:57

The mass of a proton is 18…

16:02

A free neutron beta decays…

10:05

(a) Show that the proton-d…

09:55

03:18

What is the velocity, as a…

06:31

Two protons (each with res…

02:18

A proton in a large accele…

Well, uh, wrist muscles. One electron m is equal to buying 0.11 multiplied by 10 to the power minus 30 bond kilogram and speed off light C equals 3.0 multiplied by 10 to the power eight meter per second and ah, the total rest mass energy off the electron positron pair. Ah, total energy is a cool too. Two times months off electron times C square and this is equal to to multiply by Most of electron is 9.11 multiplied by 10 to the power minus 31 Motive live I see his 3.0 Multiply by 10 to the barber ate all square and therefore total energy off the pair Physical to 1.64 Multiply by 10 to the power minus 13. Jules All right. Uh, no. Ah! Kinetic energy e is equal to gamma minus one times M c square, M C square. And here I am is the moss of proton. Therefore, we have m mass of raton and most of Britain is a call to 1.6 multiplied by its must've positron, not proton. Excuse me. 1.6 multiply returned to the power minus 27. Um, well, Soling for, uh, gamma. We have gamma physical, too divided by ah moss off Rosie Traum. Time C square less one. And this uses 1.64 multiplied by 10 to the power minus 13. Do you find it by the most of positron is 1.6. Multiply by 10 to the power minus 27. Multiply by three molted live I tend to the bar for eight whole square and therefore got more is equal to 1.1 No, we have Ah, gamma is equal to well, one divided by one divided by a squared Rudolph one minus. We squared, divided by C square and solving for re we have we is equal to see into square rode off one minus one minus one divided by normal square Let's plug in values we equals three multiply by tend to devour it into one minus one, divided by 1.1 all square and therefore we is equal to well, we is equal to 1.34 Multiply by 10 to the power seven leader for a second. Hence the velocity of the proton will be Ah, one point. Ahh. 34 multiplied by 10 to the power seven leader per second on. Right? No. Let's. Um um uh, let's find out. Uh, the gamma Well, we know that gamma can be regiones e divided by most of electron times C square. And we know that on plus one as well. And we know that he divided by massive electron time C square is equal to two. And therefore we have gamma physical 22 plus one and excuse us train. And hence the velocity off the electron will be We is equal to see into one minus, uh, one divided by gum square. Deal for V equals three. Multiply by 10 to the power eight into one minus one, divided by three square on This gives us 2.89 Multiply by 10 to the power eight meter per second. Eight meter per second.

View More Answers From This Book

Find Another Textbook

In physics, wave optics is the study of the behavior of light, or other elec…

Interference is a phenomenon in which two waves superpose to form a resultan…

(a) How much energy is released when an electron and a positron annihilate e…

An electron with a total energy of 30.0 GeV collides with a stationary posit…

A muon has a rest mass energy of $105.7 \mathrm{MeV},$ and it decays into an…

An electron with a total energy of 20.0 GeV collides with a stationary posit…

An electron has a speed of $0.750 c .$ (a) Find the speed of a proton that h…

An electron and a positron are moving toward each other and each has speed 0…

(a) Beta decay is nuclear decay in which an electron is emitted. If the elec…

An electron has a speed of 0.750$c.$ (a) Find the speed of a proton that has…

When an electron and positron annihilate, both their masses are destroyed, c…

The rest energy of an electron is 0.511 MeV. The rest energy of a proton is …

The rest energy of an electron is $0.511 \mathrm{MeV}$. The rest energy of a…

An electron has a speed of 0.750 . (a) Find the speed of a proton that has t…

The mass of a proton is 1836 times the mass of an electron.(a) A proton …

A free neutron beta decays by creating a proton, an electron, and an antineu…

(a) Show that the proton-decay reaction $\mathrm{p} \rightarrow \mathrm{e}^{…

(a) Show that the proton-decay $p \rightarrow e^{+}+\gamma$ cannot occur bec…

What is the velocity, as a fraction of $c,$ ofa. A proton with 500 GeV t…

Two protons (each with rest mass $M=1.67 \times 10^{-27} \mathrm{kg}$ ) are …

A proton in a large accelerator has a kinetic energy of 175 GeV. (a) Compare…

02:30

What is the rest energy of an electron, given its mass is $9.11 \times 10^{-…

01:26

One scheme to put nuclear weapons to nonmilitary use is to explode them unde…

02:46

Construct Your Own Problem Consider an ultrahigh-energy cosmic ray entering …

04:33

Assume one-fourth of the yield of a typical $320-\mathrm{kT}$ strategic bomb…

02:35

One of the decay modes of the omega minus is $\Omega^{-} \rightarrow \Xi^{0}…

02:03

(a) Find the total energy released in MeV in each carbon cycle (elaborated i…

01:10

Tritium is naturally rare, but can be produced by the reaction $n+^{2} \math…

05:01

What is the velocity of an electron that has a momentum of $3.04 \times 10^{…

01:22

(a) Find the charge, baryon number, strangeness, charm, and bottomness of th…

05:57

One cosmic ray neutron has a velocity of 0.250$c$ relative to the Earth. (a)…