Question

Which of the following statements is correct?

• A. Fusion of $1g$ of hydrogen gives more energy than fission of $1g$of Uranium-$235$
• B. Fusion of $1g$ of hydrogen gives less energy than fission of $1g$ of Uranium-$235$
• C. Fusion of $1g$ of hydrogen gives same energy as in fission of $1g$of Uranium-$235$
• D. Fusion of $1g$ of Uranium gives less energy than the combustion of $1ton$ of coal

Answer 1

The correct option is A

Fusion of $1\mathrm{g}$ of hydrogen gives more energy than fission of $1\mathrm{g}$of Uranium-$235$

Fusion of hydrogen and fission of Uranium-$235$ is an example of nuclear fusion and fission reactions respectively. These reactions are required very high temperature.

Mathematically:

Step 1: Fusion of $1\mathrm{g}$ of Hydrogen produces $6.4\times {10}^{11}Joules\left(J\right)$

Step 2: Fission of $1\mathrm{g}$ of one atom of Uranium-$235$ produces $202.5\mathrm{MeV}$ or $3.244\times {10}^{-11}\mathrm{J}$

then, $235\mathrm{g}$ of Uranium contains $6.023\times {10}^{23}\mathrm{atoms}$

Since, one gram of Uranium contains $\frac{6.023\times {10}^{23}}{235}$

So, the fission of one gram of uranium-$235$ generates $=$ $$\begin{gathered} \frac{6.023\times {10}^{23}}{235}\times 3.244\times {10}^{-11} \\ =8.31\times {10}^{10}\mathrm{J} \end{gathered}$$

The energy produced by fusion of $1\mathrm{g}$ of hydrogen $6.4\times {10}^{11}\mathrm{J}$ is approximate $100$ times greater than the energy produced from Uranium- $235$ is $8.31\times {10}^{10}\mathrm{J}$. Hence, the fusion of $1\mathrm{g}$ of hydrogen gives more energy than fission of $1\mathrm{g}$ of Uranium-$235$.

Step 3: Combustion of $1\mathrm{Kg}$ of coal released $3\times {10}^7\mathrm{J}$

The energy obtained from fission of Uranium-$235$ reactions is greater than the one ton of combusting coal.

Final answer:

Hence,, the statement (A) is correct.