The fission of 1 kg of uranium gives about \(10^{14}\ \mathrm{J}\) of energy. Burning 1 kg of coal gives about \(10^{7}\ \mathrm{J}\). The mass of coal that gives the same energy as the fission of 1 g of uranium is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(10^{4}\ \mathrm{kg}\)
First find the energy given by 1 g of uranium. Then divide it by the energy that 1 kg of coal gives.
Given:
\( E_{\mathrm{U}}=10^{14}\ \mathrm{J\,kg^{-1}} \)
\( E_{\mathrm{coal}}=10^{7}\ \mathrm{J\,kg^{-1}} \)
\( m_{\mathrm{U}}=1\ \mathrm{g}=10^{-3}\ \mathrm{kg} \)
\( \begin{aligned} E &= 10^{-3}\times10^{14} \\ &= 10^{11}\ \mathrm{J} \end{aligned} \)
\( \begin{aligned} m_{\mathrm{coal}} &= \frac{E}{E_{\mathrm{coal}}} \\ &= \frac{10^{11}}{10^{7}} \\ &= 10^{4}\ \mathrm{kg} \end{aligned} \)
Therefore, about \( 10^{4}\ \mathrm{kg} \) (10 tonnes) of coal must be burnt to match the fission of just 1 g of uranium.
NCERT (2026-27):
Nuclear Energy – “… Thus for the same quantity of matter, nuclear sources produce a million times more energy than a chemical source. Fission of 1 kg of uranium, for example, generates 1014 J of energy; compare it with burning of 1 kg of coal that gives 107 J.”