<< 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

A few grains of table salt were put in a cup of cold water kept at constant temperature and left undisturbed. eventually all the water tasted salty. this is due to?
Faith Reply
what is magnetism
Eze Reply
physical phenomena arising from force caused by magnets
Mohammad
is the phenomenon of attracting magnetic substance like iron, cobalt etc.
Faith
what is heat
John Reply
Heat is a form of energy where molecules move
saran
Can you please help me with some questions
Janet Reply
topic-- question
Salman
I know this is unrelated to physics, but how do I get the MCQs and essay to work. they arent clickable.
Jake Reply
20cm3 of 1mol/dm3 solution of a monobasic acid HA and 20cm3 of 1mol/dm3 solution of NaOH are mixed in a calorimeter and a temperature rise of 274K is observed. If the heat capacity of the calorimeter is 160J/K, calculate the enthalpy of neutralization of the acid.(SHCw=4.2J/g/K) Formula. (ms*cs+C)*T
Lilian Reply
why is a body moving at a constant speed able to accelerate
Lilian Reply
20cm3 of 1mol/dm3 solution of a monobasic acid HA and 20cm3 of 1mol/dm3 solution of NaOH are mixed in a calorimeter and a temperature rise of 274K is observed. If the heat capacity of the calorimeter is 160J/K, calculate the enthalpy of neutralization of the acid.(SHCw=4.2J/g/K) Formula. (ms*cs+C)*T
Lilian
because it changes only direction and the speed is kept constant
Justice
Why is the sky blue...?
Star Reply
It's filtered light from the 2 forms of radiation emitted from the sun. It's mainly filtered UV rays. There's a theory titled Scatter Theory that covers this topic
Mike
A heating coil of resistance 30π is connected to a 240v supply for 5min to boil a quantity of water in a vessel of heat capacity 200jk. If the initial temperature of water is 20°c and it specific heat capacity is 4200jkgk calculate the mass of water in a vessel
fasawe Reply
A thin equi convex lens is placed on a horizontal plane mirror and a pin held 20 cm vertically above the lens concise in position with its own image the space between the undersurface of d lens and the mirror is filled with water (refractive index =1•33)and then to concise with d image d pin has to
Azummiri Reply
Be raised until its distance from d lens is 27cm find d radius of curvature
Azummiri
what happens when a nuclear bomb and atom bomb bomb explode add the same time near each other
FlAsH Reply
A monkey throws a coconut straight upwards from a coconut tree with a velocity of 10 ms-1. The coconut tree is 30 m high. Calculate the maximum height of the coconut from the top of the coconut tree? Can someone answer my question
Fatinizzah Reply
v2 =u2 - 2gh 02 =10x10 - 2x9.8xh h = 100 ÷ 19.6 answer = 30 - h.
Ramonyai
why is the north side is always referring to n side of magnetic
sam Reply
who is a nurse
Chilekwa Reply
A nurse is a person who takes care of the sick
Bukola
a nurse is also like an assistant to the doctor
Gadjawa
explain me wheatstone bridge
Malik Reply
good app
samuel
Wheatstone bridge is an instrument used to measure an unknown electrical resistance by balancing two legs of a bridge circuit, one leg of which includes the unknown component.
MUHD
Rockwell Software is Rockwell Automation’s "Retro Encabulator". Now, basically the only new principle involved is that instead of power being generated by the relative motion of conductors and fluxes, it’s produced by the modial interaction of magneto-reluctance and capacitive diractance. The origin
Chip
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