Mass-energy Equivalence

Einstein's mass-energy equivalence states that a rest mass $m$ carries energy $E=m{c}^2$, so complete conversion of matter to radiation releases this entire amount. The mass must first be expressed in kilograms: $2$ g $=2\times 10^{-3}$ kg. Substituting into $E=m{c}^2$ with $c=3\times 10^8$ m/s gives $E=(2\times 10^{-3})\times (3\times 10^8{)}^2=(2\times 10^{-3})\times (9\times 10^{16})=1.8\times 10^{14}$ J. The value $6\times 10^5$ J wrongly uses $E=mc$ instead of $m{c}^2$. The value $1.8\times 10^{11}$ J forgets to convert grams to kilograms, using $2$ instead of $0.002$ inconsistently. The value $9\times 10^{16}$ 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 $E=m{c}^2$ 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 $\sim 10^{14}$ J, comparable to the output of a large power plant over hours, reflecting the huge factor $c^2$.