JEE MAIN - Physics (2024 - 9th April Morning Shift - No. 16)
Explanation
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: $$5.6 \times 10^{26} \mathrm{~MeV}$$
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