Mass-energy Equivalence

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In a hypothetical process, 2 grams of matter is completely converted into electromagnetic energy in accordance with Einstein's mass-energy relation. Taking the speed of light as 3 × 10^8 m/s, how much energy is liberated?

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Einstein's mass-energy equivalence states that a rest mass $m$ carries energy $E = mc^2$, so complete conversion of matter to radiation releases this entire amount. The mass must first be expressed in kilograms: $2$ g $= 2	imes10^{-3}$ kg. Substituting into $E = mc^2$ with $c = 3	imes10^8$ m/s gives $E = (2	imes10^{-3}) 	imes (3	imes10^8)^2 = (2	imes10^{-3}) 	imes (9	imes10^{16}) = 1.8	imes10^{14}$ J. The value $6	imes10^5$ J wrongly uses $E = mc$ instead of $mc^2$. The value $1.8	imes10^{11}$ J forgets to convert grams to kilograms, using $2$ instead of $0.002$ inconsistently. The value $9	imes10^{16}$ J is simply $c^2$ and omits the mass factor altogether. Such complete conversion of rest mass into energy occurs in practice only in matter-antimatter annihilation, since ordinary nuclear reactions transform just a tiny fraction of the rest mass, yet the same relation $E = mc^2$ governs every nuclear energy release through the binding-energy mass defect. This applies the NCERT mass-energy relation underlying nuclear energy release. A plausibility check confirms the enormous magnitude: even a couple of grams yields $\sim10^{14}$ J, comparable to the output of a large power plant over hours, reflecting the huge factor $c^2$.

Mass-energy Equivalence

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