Sol. Since the neutron and boron are both initially at rest, the total momentum before the reaction is zero and afterward is also zero. Therefore,

M Li v Li = M He v He

We solve this for v Li and substitute it into the equation for kinetic energy. We can use classical kinetic energy with little error, rather than relativistic formulas, because v He = 9.30 × 10 6 m/s is not close to the speed of light c and v Li will be even less since M Li > M He . Thus we can write :

K Li = M Li = M Li =

We put in numbers, changing the mass in u to kg and recalling that 1.60 × 10 13 J = 1 MeV:

K Li =

= 1.64 × 10 –13 J = 1.02 MeV

We are given the data K a = K X = 0, so Q = K Li + K He , where

K He = M He = (4.0026)(1.66 × 10 –27 )(9.30 × 10 6 ) 2 = 2.87 × 10

–13 J = 1.80 MeV

Hence, Q = 1.02 MeV + 1.80 MeV = 2.82 MeV.