Question

The energy released per fission reaction of ${\text{U}}^{235}$ is $200\text{MeV}$. Find the energy released by the fission of $1\text{g}$ of ${\text{U}}^{235}$.
$(\text{Avogadro number},N_A=6.023\times {10}^{23})$

• A. $8.202\times {10}^{14}\text{J}$
• B. $8.202\times {10}^{12}\text{J}$
• C. $8.202\times {10}^{10}\text{J}$
• D. $8.202\times {10}^8\text{J}$

Answer 1

The correct option is C $8.202\times {10}^{10}\text{J}$

Total energy released,
$E=n{E}_1---\left(1\right)$

Where,
$n-\text{number of atoms in}1\text{g}\text{of}{\text{U}}^{235}$

$E_1-\text{Energy released in one fission}$

We know that,

$n=\frac{m}{M}{N}_A---\left(2\right)$

Substituting $\left(2\right)\text{in}\left(1\right)$

$E=\frac{m{N}_A}{M}{E}_1$

Here, $m=1\text{g}$, $M=235\text{g}$,
$E_1=200\text{MeV}=200\times {10}^{-13}\text{J}$

$\Rightarrow E=\frac{1\times 6.023\times {10}^{23}\times 200\times 1.6\times {10}^{-13}}{235}$

$\Rightarrow E=8.2\times {10}^{10}\text{J}$

Hence, option $\left(C\right)$ is correct.