Question

In a nuclear reactor, energy is produced by the following process:

${}_1{H}^2{+}_1{H}^2{\to }_1{H}^3+P{}^{}{}_1{H}^3{+}_1{H}^2{\to }_{2}H{e}^4+n$

The reactor produces a power of ${10}^{10}$ MW with 50% efficiency. The number of deutrons required to run the reactor for one year will be apporoximately: $m\left(1_H^2\right)$ = 2.014 u. m(p) = 1.007 u. m(n) = 1.008u. $m\left(2_H{e}^4\right)$ = 4.00 1u

• A. $5\times {10}^{35}$
• B. $5\times {10}^{32}$
• C. $5\times {10}^{38}$
• D. $5\times {10}^{40}$

Answer 1

The correct option is A

$5\times {10}^{35}$

For each reaction involving both the processes, mass defect
$=3\times 2.014-4.001-1.007=0.028u$
Energy released per deutron $=\frac{931.5\times 0.028}{3}MeV$
Let n be the number of deutrons required
Total energy $-\frac{931.5\times 0.026}{3}\times nMeV-\frac{P\times t}{\eta }-\frac{{10}^{16}\times 365\times 24\times 60\times 60}{0.5}$
$n=5\times {10}^{35}$