Q157 / 160 · TS EAMCET 2022 (20 Jul Shift 2) · Physics

What will be the energy released in joule, in the process of fission by $1 \mathrm{mg}$ of ${ }_{92}^{240} \mathrm{U}$. Assume energy release per fission is $200 \mathrm{MeV}$. [useAvogadro's number as $6 \times 10^{23}$ and $1 \mathrm{eV}=1.6 \times 10^{-19} \mathrm{~J}$ ]

  • A
    $6.2 \times 10^7 \mathrm{~J}$
  • B
    $7.0 \times 10^7 \mathrm{~J}$
  • Correct answer
    C
    $8.0 \times 10^7 \mathrm{~J}$
  • D
    $8.2 \times 10^7 \mathrm{~J}$

Solution

Let $\mathrm{n}=$ number of moles Then, $\mathrm{n}=\frac{\mathrm{m}}{\mathrm{M}}=\frac{\mathrm{N}}{\mathrm{N}_{\mathrm{A}}}$ $\begin{aligned} & \Rightarrow \mathrm{N}=\frac{\mathrm{m}}{\mathrm{M}} \times \mathrm{N}_{\mathrm{A}} \\ & \Rightarrow \mathrm{N}=\frac{1 \times 10^{-3}}{240} \times\left(6 \times 10^{23}\right) \Rightarrow \mathrm{N}=2.5 \times 10^{18} \end{aligned}$ So, energy released $=\mathrm{N} \times 200 \mathrm{MeV}$ $=2.5 \times 10^{18} \times 200 \times 1.6 \times 10^{-13}=8 \times 10^7 \mathrm{~J}$

Hence, the correct answer is option: 'C'.

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