QJEEM24Ph94a6: JEE Main 2024 Physics - Class 12 JEEM24Ph94a6 Solution: The energy equivalent of of substance is :

To determine the energy equivalent of a mass, we use Einstein's mass-energy equivalence principle given by the equation:

$E = mc^2$

where:

- $E$ is the energy

- $m$ is the mass

- $c$ is the speed of light in a vacuum, which is approximately $3 \times 10^8 \mathrm{~m/s}$

Given the mass $m = 1 \mathrm{~g} = 1 \times 10^{-3} \mathrm{~kg}$ , we can substitute these values into the equation:

$E = (1 \times 10^{-3} \mathrm{~kg}) \times (3 \times 10^8 \mathrm{~m/s})^2$

Calculating this, we get:

$E = 1 \times 10^{-3} \times 9 \times 10^{16}$

$E = 9 \times 10^{13} \mathrm{~J}$

Next, to convert this energy into electron volts ( $\mathrm{eV}$ ), we use the conversion factor: $1 \mathrm{~J} = 6.242 \times 10^{12} \mathrm{~MeV}$ .

Therefore:

$E = 9 \times 10^{13} \mathrm{~J} \times 6.242 \times 10^{12} \mathrm{~MeV/J}$

Calculating this, we get:

$E = 5.6178 \times 10^{26} \mathrm{~MeV}$

Therefore, the energy equivalent of $1 \mathrm{~g}$ of a substance is:

Option A: $5.6 \times 10^{26} \mathrm{~MeV}$