Q76 / 90 · JEE Main 2024 (08 Apr Shift 1) · Physics

Binding energy of a certain nucleus is $18 \times 10^8 \mathrm{~J}$. How much is the difference between total mass of all the nucleons and nuclear mass of the given nucleus:

  • A
    $10 \mu \mathrm{g}$
  • Correct answer
    B
    $20 \mu \mathrm{g}$
  • C
    $0.2 \mu \mathrm{g}$
  • D
    $2 \mu \mathrm{g}$

Solution

$\begin{aligned} & \Delta \mathrm{mc}^2=18 \times 10^8 \\ & \Delta \mathrm{m} \times 9 \times 10^{16}=18 \times 10^8 \\ & \Delta \mathrm{m}=2 \times 10^{-8} \mathrm{~kg}=20 \mu \mathrm{g}\end{aligned}$

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

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