Question

The energy released by 1 kg uranium fission is

• A.
  $8\times {10}^{10}J$
• B.
  $8\times {10}^{13}J$
• C.
  $4\times {10}^{10}J$
• D.
  $4\times {10}^{13}J$

Answer 1

The correct option is B

$8\times {10}^{13}J$
The mass of one mole $(6.023\times 1023atoms)$ of ${}_{92}{U}^{235}$ is 235 g.

$\therefore$ Number of atoms in 1 kg of ${}_{92}{U}^{235},n=\frac{1\times 1000}{235}\times 6.023\times {10}^{23}$

Energy released per atom in $U^{235}$ fission reaction = 200 MeV

The energy released by 1 kg uranium fission can be calculated as:
$\Delta U=n\times 200MeV=n\times 200\times 1.6\times {10}^{-13}J=\frac{1000}{235}\times 6.023\times {10}^{23}\times 200\times 1.6\times {10}^{-13}J=8\times {10}^{13}J$



Hence, the correct answer is option (b).