Question

In a thermonuclear reaction, ${10}^{-3}\text{kg}$ of $\text{hydrogen}$ is converted into $0.99\times {10}^{-3}\text{kg}$ of $\text{helium}$. If the efficiency of the generator is $50\text{\%}$, the electrical energy generated in $\text{kWh}$ is

• A. $1.25\times {10}^5$
• B. $1.5\times {10}^5$
• C. $1.35\times {10}^5$
• D. $1\times {10}^5$

Answer 1

The correct option is A $1.25\times {10}^5$

Efficiency, $\eta =\frac{E_{out}}{E_{in}}$

Here, energy is generated due to the difference in mass of the reactants and products,

$\Rightarrow \Delta m=(1-0.99)\times {10}^{-3}\text{kg}$

$\Rightarrow \Delta m=0.01\times {10}^{-3}\text{kg}$

By Einstein's mass energy equivalence,

$E_{in}=\Delta m\times c^2$

Given that, $\eta =50\text{\%}$

$\Rightarrow E_{out}=\eta E_{in}=\eta \left(\Delta m\right)c^2$

$\Rightarrow E_{out}=\frac{50}{100}(0.01\times {10}^{-3})\times (3\times {10}^8{)}^2$

$\Rightarrow E_{out}=\frac{9}{2}\times {10}^{11}\text{J}$

We know that, $1\text{kWh}=36\times {10}^5\text{J}$

$\Rightarrow E_{out}=4.5\times {10}^{11}\times \frac{1}{36\times {10}^5}\text{kWh}$

$\Rightarrow E_{out}=0.125\times {10}^6\text{kWh}$

$\Rightarrow E_{out}=1.25\times {10}^5\text{kWh}$

Hence, option $\left(A\right)$ is correct.