<< Chapter < Page Chapter >> Page >

A photon decays into an electron-positron pair. What is the kinetic energy of the electron if its speed is 0.992 c size 12{c} {} ?

Answer

KE rel = ( γ 1 ) mc 2 = 1 1 v 2 c 2 1 mc 2 = 1 1 ( 0.992 c ) 2 c 2 1 ( 9.11 × 10 31 kg ) ( 3.00 × 10 8 m/s ) 2 = 5.67 × 10 13 J
Got questions? Get instant answers now!

Section summary

  • Relativistic energy is conserved as long as we define it to include the possibility of mass changing to energy.
  • Total Energy is defined as: E = γmc 2 , where γ = 1 1 v 2 c 2 .
  • Rest energy is E 0 = mc 2 , meaning that mass is a form of energy. If energy is stored in an object, its mass increases. Mass can be destroyed to release energy.
  • We do not ordinarily notice the increase or decrease in mass of an object because the change in mass is so small for a large increase in energy.
  • The relativistic work-energy theorem is W net = E E 0 = γ mc 2 mc 2 = γ 1 mc 2 .
  • Relativistically, W net = KE rel , where KE rel is the relativistic kinetic energy.
  • Relativistic kinetic energy is KE rel = γ 1 mc 2 , where γ = 1 1 v 2 c 2 . At low velocities, relativistic kinetic energy reduces to classical kinetic energy.
  • No object with mass can attain the speed of light because an infinite amount of work and an infinite amount of energy input is required to accelerate a mass to the speed of light.
  • The equation E 2 = ( pc ) 2 + ( mc 2 ) 2 relates the relativistic total energy E and the relativistic momentum p . At extremely high velocities, the rest energy mc 2 becomes negligible, and E = pc .

Conceptual questions

How are the classical laws of conservation of energy and conservation of mass modified by modern relativity?

Got questions? Get instant answers now!

What happens to the mass of water in a pot when it cools, assuming no molecules escape or are added? Is this observable in practice? Explain.

Got questions? Get instant answers now!

Consider a thought experiment. You place an expanded balloon of air on weighing scales outside in the early morning. The balloon stays on the scales and you are able to measure changes in its mass. Does the mass of the balloon change as the day progresses? Discuss the difficulties in carrying out this experiment.

Got questions? Get instant answers now!

The mass of the fuel in a nuclear reactor decreases by an observable amount as it puts out energy. Is the same true for the coal and oxygen combined in a conventional power plant? If so, is this observable in practice for the coal and oxygen? Explain.

Got questions? Get instant answers now!

We know that the velocity of an object with mass has an upper limit of c size 12{c} {} . Is there an upper limit on its momentum? Its energy? Explain.

Got questions? Get instant answers now!

Given the fact that light travels at c size 12{c} {} , can it have mass? Explain.

Got questions? Get instant answers now!

If you use an Earth-based telescope to project a laser beam onto the Moon, you can move the spot across the Moon’s surface at a velocity greater than the speed of light. Does this violate modern relativity? (Note that light is being sent from the Earth to the Moon, not across the surface of the Moon.)

Got questions? Get instant answers now!

Problems&Exercises

What is the rest energy of an electron, given its mass is 9 . 11 × 10 31 kg ? Give your answer in joules and MeV.

8.20 × 10 14 J

0.512 MeV

Got questions? Get instant answers now!

Find the rest energy in joules and MeV of a proton, given its mass is 1 . 67 × 10 27 kg .

Got questions? Get instant answers now!

If the rest energies of a proton and a neutron (the two constituents of nuclei) are 938.3 and 939.6 MeV respectively, what is the difference in their masses in kilograms?

2 . 3 × 10 30 kg size 12{2 "." 3 times "10" rSup { size 8{ - "30"} } `"kg"} {}

Got questions? Get instant answers now!

Questions & Answers

material that allows electric current to pass through
Deng Reply
material which don't allow electric current is called
Deng
insulators
Covenant
how to study physic and understand
Ewa Reply
what is conservative force with examples
Moses
what is work
Fredrick Reply
the transfer of energy by a force that causes an object to be displaced; the product of the component of the force in the direction of the displacement and the magnitude of the displacement
AI-Robot
why is it from light to gravity
Esther Reply
difference between model and theory
Esther
Is the ship moving at a constant velocity?
Kamogelo Reply
The full note of modern physics
aluet Reply
introduction to applications of nuclear physics
aluet Reply
the explanation is not in full details
Moses Reply
I need more explanation or all about kinematics
Moses
yes
zephaniah
I need more explanation or all about nuclear physics
aluet
Show that the equal masses particles emarge from collision at right angle by making explicit used of fact that momentum is a vector quantity
Muhammad Reply
yh
Isaac
A wave is described by the function D(x,t)=(1.6cm) sin[(1.2cm^-1(x+6.8cm/st] what are:a.Amplitude b. wavelength c. wave number d. frequency e. period f. velocity of speed.
Majok Reply
what is frontier of physics
Somto Reply
A body is projected upward at an angle 45° 18minutes with the horizontal with an initial speed of 40km per second. In hoe many seconds will the body reach the ground then how far from the point of projection will it strike. At what angle will the horizontal will strike
Gufraan Reply
Suppose hydrogen and oxygen are diffusing through air. A small amount of each is released simultaneously. How much time passes before the hydrogen is 1.00 s ahead of the oxygen? Such differences in arrival times are used as an analytical tool in gas chromatography.
Ezekiel Reply
please explain
Samuel
what's the definition of physics
Mobolaji Reply
what is physics
Nangun Reply
the science concerned with describing the interactions of energy, matter, space, and time; it is especially interested in what fundamental mechanisms underlie every phenomenon
AI-Robot
Practice Key Terms 3

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'College physics' conversation and receive update notifications?

Ask