A star initially has `10^(40) ` deuterons. It produces energy via the process `_(1)H^(2) + _(1)H^(2) + rarr _(1) H^(3) + p. `and `_(1)H^(2) + _(1)H^(3) + rarr _(2) He^(4) + n` .If the average power radiated by the state is `10^(16) W` , the deuteron supply of the star is exhausted in a time of the order of .
The masses of the nuclei are as follows:
`M(H^(2)) = 2.014 amu,`
`M(p) = 1.007 amu, M(n) = 1.008 amu, M(He^(4)) = 4.001 amu`.

Options

A. `10^(6)s`
B. `10^(8)s`
C. `10^(12)s`
D. `10^(16)s`

Answer

C

Explanation

mass defect `._(Delta)m=0.026 "amu"`
Energy released per reaction is
`=0.026xx931.5 MeV=24.2 MeV`
`=3.87xx10^(-12)J`
Energy released by consuming `10^(40)` deuterons is
`=3.87xx10^(-12)xx(10^(40))/(3)=12.9xx10^(28)J`
Power=energy/time