<< 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

can a wheat stone bridge balance
jharana Reply
what is Norton's theorm
jharana
an atom is symply a smallest unsplittable particle that makes up a compound
levison Reply
what is atom
Ismaila Reply
nano parricles are arranging periodic
Bala
Water is flowing in a pipe with a varying cross-sectional area, and at all points the water completely fills the pipe. At point 1 the cross-sectional area of the pipe is 0.077 m2, and the magnitude of the fluid velocity is 3.50 m/s. (a) What is the fluid speed at points in the pipe where the cross
fagbeji Reply
A particle behave like a wave and we do not why?
WAQAR
what's the period of velocity 4cm/s at displacement 10cm
Andrew Reply
What is physics
LordRalph Reply
the branch of science concerned with the nature and properties of matter and energy. The subject matter of physics includes mechanics, heat, light and other radiation, sound, electricity, magnetism, and the structure of atoms.
Aluko
and the word of matter is anything that have mass and occupied space
Aluko
what is phyices
Aurang Reply
Whats the formula
Okiri Reply
1/v+1/u=1/f
Aluko
what aspect of black body spectrum forced plank to purpose quantization of energy level in its atoms and molicules
Shoaib Reply
a man has created by who?
Angel Reply
What type of experimental evidence indicates that light is a wave
Edeh Reply
double slit experiment
Eric
The S. L. Unit of sound energy is
Chukwuemeka Reply
Hertz
jharana
what's the conversation like?
ENOBONG Reply
some sort of blatherring or mambo jambo you may say
muhammad
I still don't understand what this group is all about oo
ENOBONG
no
uchenna
ufff....this associated with physics ..so u can ask questions related to all topics of physics..
muhammad
what is sound?
Bella
what is upthrust
Mercy Reply
what is upthrust
Olisa
Up thrust is a force
Samuel
upthrust is a upward force that acts vertical in the ground surface.
Rodney
yes rodney's answer z correct
Paul
what is centre of gravity?
Paul
you think the human body could produce such Force
Anthony
what is wave
Bryan Reply
mirobiology
Angel
Practice Key Terms 3

Get the best College physics course in your pocket!





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