The energy equivalent of $1 \mathrm{~g}$ of substance is :

The energy equivalent of $1 \mathrm{~g}$ of substance is :
  1. $5.6 \times 10^{12} \mathrm{MeV}$
  2. $5.6 \times 10^{26} \mathrm{MeV}$
  3. $11.2 \times 10^{24} \mathrm{MeV}$
  4. $5.6 \mathrm{eV}$

Solution

$\mathrm{E}=\mathrm{mC}^2$ $\begin{aligned} & \Rightarrow \mathrm{E}=\left(1 \times 10^{-3}\right) \times\left(3 \times 10^8\right)^2 \mathrm{~J} \\ & \Rightarrow \mathrm{E}=\left(10^{-3}\right)\left(9 \times 10^{16}\right)\left(6.241 \times 10^{18}\right) \mathrm{eV} \\ & \mathrm{E}=56.169 \times 10^{31} \mathrm{eV} \\ & \mathrm{E} \approx 5.6 \times 10^{26} \mathrm{MeV} \\ & \end{aligned}$

Asked in: JEE Main 2024 (09 Apr Shift 1)

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