It is found that if a neutron suffers an elastic collinear collision with deuterium at rest, fractional loss of its energy is `p_(d)`, while for its similar collision with carbon nucleus at rest, fractional loss of energy is `p_(c )`. The values of `p_(d)` and `p_(c )` are respectively :

Options

A. (0,0)
B. (0,1)
C. `(.89, .28)`
D. `(.28, .89)`

Answer

C

Explanation

Collision with deuterium
`mv+ 0= mv_(1)+2mv_(2)` ...(i)
`rArr v_(2)-v_(1)=v` [Since, e=1] ...(ii)
from (i) and (ii)
`v_(1)= (-v)/(3)`
`P_(d)= ((1)/(2) mv^(2)- (1)/(2) mv_(1)^(2))/((1)/(2)mv^(2))= (8)/(9)= 0.89`
Collision with carbon Nucleus
`mv+ 0= mv_(1) + 12mv_(2)` ...(iii)
`v= v_(2)- v_(1) [therefore e=1]` ...(iv)
From (iii) and (iv)
`v_(1)= (-11)/(13)v`
`P_(C)= ((1)/(2) mv^(2)- (1)/(2) m((11)/(13)v)^(2))/((1)/(2) mv^(2))= (48)/(169)= 0.28`