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C.E
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1. a. An electron of rest mass (0.511Mev) is accelerated in a linear accelerator so it has a total energy of 40 Gev.
i).What fraction of the total energy is kinetic energy?
ii).what is the reletivistic linear momentum of the electron?
iii).What is its relativistic mass?
b.A particle of rest mass m travels so that its total energy is twice its rest mass energy. It collides with a particle of rest mass m and forms a composite particle.
i). What is the momentum of each of the initial particles?
ii).What is the momentum of the new particle produced in the collision.
iii).What is the rest mass of the new particle
3. Here is my attempt at part a, there are a few things I am unsure on firstly, in answering this question I have assumed potential energy is negligeable, i.e. there is only kinetic and rest mass energy, is that ok? Secondly I am a bit worried by the fact I keep getting 40 as an answer and finally, I was unsure on units, what are the units of gamma?
a. (i). (40 x 10^9 - 0.511 x 10^6)/40 x 10^9 =0.99999.
ii) E^2=p^2c^2 +m^2c^4
so p=40Gev/c
iii).E=gmc^2 where g is gamma.
Therefore g= (40x 10^9)/ 0.511 x 10^6) =78278.
Hence relativistic mass= 78278 x 0.511 x 10^-3= 40 Gev/c^2.
Here is part b.
b. (i). stationary particle: 0.
moving particle:mc^2sqrt(3) using the same equation as in aii.
(ii) sqrt(3)mc^2 by conservation laws.
(iii)Total energy mc^2 + 2mc^2 =3mc^2
rest energy=sqrt(total energy^2-(momentumxc)^2)
=sqrt(6m^2c^4)=mc^2sqrt(6)
Have I done this question right?
i).What fraction of the total energy is kinetic energy?
ii).what is the reletivistic linear momentum of the electron?
iii).What is its relativistic mass?
b.A particle of rest mass m travels so that its total energy is twice its rest mass energy. It collides with a particle of rest mass m and forms a composite particle.
i). What is the momentum of each of the initial particles?
ii).What is the momentum of the new particle produced in the collision.
iii).What is the rest mass of the new particle
3. Here is my attempt at part a, there are a few things I am unsure on firstly, in answering this question I have assumed potential energy is negligeable, i.e. there is only kinetic and rest mass energy, is that ok? Secondly I am a bit worried by the fact I keep getting 40 as an answer and finally, I was unsure on units, what are the units of gamma?
a. (i). (40 x 10^9 - 0.511 x 10^6)/40 x 10^9 =0.99999.
ii) E^2=p^2c^2 +m^2c^4
so p=40Gev/c
iii).E=gmc^2 where g is gamma.
Therefore g= (40x 10^9)/ 0.511 x 10^6) =78278.
Hence relativistic mass= 78278 x 0.511 x 10^-3= 40 Gev/c^2.
Here is part b.
b. (i). stationary particle: 0.
moving particle:mc^2sqrt(3) using the same equation as in aii.
(ii) sqrt(3)mc^2 by conservation laws.
(iii)Total energy mc^2 + 2mc^2 =3mc^2
rest energy=sqrt(total energy^2-(momentumxc)^2)
=sqrt(6m^2c^4)=mc^2sqrt(6)
Have I done this question right?
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