An electron has speed 099c in the lab frame where c is the...

An electron has speed 0.99c in the lab frame, where c is the speed of light. (a) What is the momentum of the electron in SI units? Make sure to include the units. (b) Find the mass of the electron in units of MeV/c 2 . (c) What is the momentum of the electron in units of MeV/c? (d) What is the kinetic energy of the electron in units of MeV? (e) What is the total relativistic energy of the electron in MeV?

Transcript

00:01 In this question, the speed of electron is given, that is being, this is 0 .99c, and rest mass is given, rest mass of electron, that is equal to m .0, that is 9 .1 multiplied by 10 power minus 31 kg.

00:18 Okay.

00:19 So we have to calculate various things.

00:21 So in the a part, we have to calculate the momentum, that is mv, which is m not multiplied by v divided by 1 minus v squared divided by c square, that is equal to.

00:30 That is 9 .1 multiplied by 10 power minus 31 multiplied by 0 .99 multiplied by 3 multiplied by 10 power 8 divided by this is root of 1 minus v squared 2 .99 and its whole square.

00:46 Solving this value we will get our momentum that is 1 .916 multiplied by 10 power minus 21 p .g meter per second so here what is the momentum this momentum is 1 .916 multiplied by 10.

01:00 10 power minus 21 kg meter per second so this is the answer for the a part now we will solve for the b part in which we know that e is equal to what m c square if we calculate for the mass mass is equals to e divided by c square that is so this value will be equal to what so solving this we get here the mass okay so we have to calculate here the mass so first of all what is this equals to e no equal equals to m0 c squared divided by root of 1 minus v squared divided by c square that is equals to 9 .1 multiplied by 10 power minus 31 multiplied by this is 9 multiplied by 10 power 16 divided by this is root of 1 minus 0 .99 square so solving this value we get our energy that is equals to 3 .63 mega electron bolt we have to calculate the mass for mass here is equal to 3 .63 mega electron volt per bough per c square okay now we will have to calculate the momentum for the realistic particle okay so here this e is equal to momentum multiplied by the speed that is p will be equals to e divided by c that is equal to 3 .63 mega electron volt per b so this is for the momentum now we have to calculate the kinetic energy kinetic energy which is equivalent to to mc square minus m0c square.

02:35 So here this value is equals to m0c square that is root of 1 minus v squared divided by c square minus 1...

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