Burning 1 kg of coal gives \(10^{7}\ \mathrm{J}\) of energy. Taking \(c=3\times10^{8}\ \mathrm{m\,s^{-1}}\), the mass that is changed into energy in this burning is about
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(1.1\times10^{-10}\ \mathrm{kg}\)
A chemical reaction also changes a small amount of mass into energy. The energy and the mass are related by \( E=mc^{2} \). So the mass changed into energy is \( m=E/c^{2} \).
\( \begin{aligned} m &= \frac{E}{c^{2}} \\ &= \frac{10^{7}}{(3\times10^{8})^{2}} \\ &= \frac{10^{7}}{9\times10^{16}} \\ &= 1.1\times10^{-10}\ \mathrm{kg} \end{aligned} \)
From the above, \( m \) is only about \( 10^{-10} \) of the mass of the coal. Hence, the loss of mass in burning is far too small to notice.
NCERT (2026-27):
Nuclear Energy – “… compare it with burning of 1 kg of coal that gives 107 J.”
Mass – Energy – “Einstein gave the famous mass-energy equivalence relation”
\( E=mc^{2} \)\( \qquad (13.6) \)