Question

(b) A way to measure neutron energy is to have neutron elastically scatter off a He-3 nucleus. This helium isotope has 2 protons and 1 neutron in its nucleus. Find the fraction of the original energy of the incident neutron that was given to the helium nucleus.

Answer 1

The collision is elastic and we take it as head on.

mass of neutron = m

mass of He-3 = 3m

let v be the speed of neutron before collision

total momentum before collision = mv

let v1 and v2 be the speeds of neutron and He-3 after collision

total monetum after collision = mv1 + 3mv2

momentum is conserved, hence

mv = mv1 + 3mv2 ; v = v1 + 3v2 -- (1)

sicne it is elastic collision KE is also consrved

0.5 mv² = 0.5 mv1² +0.5*3mv2²

i.e v² = v1² + 3v2² ----- (2)

solving 1 and 2 we get v₂ = -v1 = v/2

total intial energy = 1/2 mv²

energy given to He-3 =1/2* 3m*(v/2)² = 3/8 mv²  

3/4 of intial energy is given to He-3 nucleus during collision.