You are at the controls of a particle accelerator, sending a beam of 1.80×107 m/s protons (mass m) at a gas target of an unknown element. Your detector tells you that some protons bounce straight back after a collision with one of the nuclei of the unknown element. All such protons rebound with a speed of 1.50×107 m/s. Assume that the initial speed of the target nucleus is negligible and the collision is elastic.

Explanation:

mass of proton = m

initial velocity, u1 = 1.80 x 10^7 m/s

final velocity, v1 = - 1.5 x 10^7 m/s

(a)

Let m' is the mass of unknown nucleus.

By use of conservation of energy

m' = 11 m

Thus, the mass of unknown nucleus is 11 times the mass of proton.

(b)

By use of conservation of momentum

m x u1 + m' x 0 = m x v1 + m' x v'

where, v' is the velocity of unknown nucleus after collision

m x 1.8 x 10^7 = - m x 1.5 x 10^7 + 11 m x v'

3.3 m x 10^7 = 11 m x v'

v' = 3 x 10^6 m/s  

Thus, the velocity of unknown nucleus after collision is 3 x 10^6 m/s