Question

Relativity question

protons with total energy 0.9TeV travel around a circle circumference 6.86 km. Show that a magnetic field of strength 0.44 T is needed to keep them moving around the circle. if protons made to collide with a stationary hydrogen target, show the largest mass of particle that can be produced is 41 GeV.

Answer 1

Since, theproton is moving at a very high speed, thekinetic energy is very high as compared to its rest mass energy. 900GeV + 0.93 88GeV)-(900GeV). (0.93 83GeV /e* ). c4 Rest mass of proton is: 938.3 MeVc 938.3x10 TeVc2 But total energy is 0.9 TeV Hence E can be approxim ated as pc E-pc For proton moving in a circul ar path, under action of magnetic field, it must obey: GeV m2-811689.2798-[810000+0.8804 1688.3994Gevc41.05GeVIcGee eR eR Using p-EC, we obtain 0.9 x10 ev 0.437T 0.441 ceR 3x10° xe x6.86 x 10 2) Since the hydrogen atom is stationary, momentum is zero. Hence total energy is equal to its rest mass energy Similarly for proton, it is given that E, = 0 9TeV = 900GeV Let the total energy of the particle produced be E. m is the mass of the particle fomed, p is its momentum. By conservation ofmomentum initial momentum must be equal to final momentum Initial momentum is just the momentum of protons( since hydrogen is at rest). So magnitude of protons momentum must be equal to magnitude of momentum of the particle. Hence Working with equation (1) replace particle momentum by proton's momentum)