Question

7. In a proton linear accelerator, protons are accelerated to have a kinetic energy of 520 MeV. What is the speed of these protons? (The rest mass of a proton is 1.67 × 10 − 27 kg.) 6.7652 c

8. In a proton linear accelerator, protons are accelerated to have a kinetic energy of 5.20 × 10 − 11 J. What is their relativistic momentum? 2.2477e-27 kg.m/s

Answer 1

7.

relativistic kE is given by

kE = m c ( 1 / sqrt ( 1 - v^2/c^2) - 1)

520* 10^-13 = 1.67* 10^-27* 3* 10^8* ( 1 / sqrt ( 1 - v^2/c^2) - 1)

sqrt ( 1- v^2/c^2) = 0.742956

v = 0.6693 c

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8.

E = 5.2* 10^-11 = 520* 10^-13 J

will follow same procedure for velocity as above

v = 0.6693 c

now relativistic momentum

P = m v / sqrt( 1 - v^2/c^2)

P = 1.67* 10^-27* 0.6693* 3* 10^8 / sqrt ( 1 - 0.6693^2)

P = 1.5* 10^-19 kg m/s

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