Question

The ratio of the energy released by \(4\) kg of hydrogen at room temperature to the heat generated by \(23.5\) kg of \({}^{235}\text{U}\) in the nuclear reactor by fission process is (Assume energy released per fusion is \(26\) MeV and that per fission is \(200\) MeV)

• A. \(5:13\)
• B. \(1:26\)
• C. \(13:10\)
• D. \(10:13\)
• E. \(26:1\)

Hint:

Convert given masses into number of reactions first, then multiply by energy per reaction.

Answer 1

The Correct Option is D

For \(4\) kg hydrogen: \[ 4\text{ kg}=4000\text{ g} \] Hydrogen molar mass is \(1\text{ g/mol}\), so number of moles: \[ 4000 \] Number of hydrogen atoms: \[ 4000N_A \] Since \(4\) hydrogen nuclei make one fusion event, number of fusion reactions: \[ \frac{4000N_A}{4}=1000N_A \] Energy from fusion: \[ E_f = 1000N_A \times 26 \] For \(23.5\) kg uranium: \[ 23.5\text{ kg}=23500\text{ g} \] Moles of \({}^{235}\text{U}\): \[ \frac{23500}{235}=100 \] Number of fission events: \[ 100N_A \] Energy from fission: \[ E_{fis}=100N_A\times 200 \] Ratio: \[ E_f:E_{fis}=(1000\times 26):(100\times 200) \] \[ =26000:20000=13:10 \] So the direct calculation gives: \[ \boxed{13:10} \] which corresponds to option (C), not (D).