Question

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

• A. $1.3\times {10}^5$
• B. $1.25\times {10}^5$
• C. $1.5\times {10}^5$
• D. ${10}^5$

Answer 1

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

The efficiency of the reactor is,

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

$E_{out}=\eta E_{in}$

$E_{out}=\eta \Delta m{c}^2$

Substituting the data given,

$E_{out}=\frac{50}{100}\times (1-0.99)\times {10}^{-3}\times 9\times {10}^{16}$

$=\frac{1}{2}\times 0.01\times {10}^{-3}\times 9\times {10}^{16}$

$=4.5\times {10}^{11}\text{J}$

$=\frac{45\times {10}^{10}}{36\times {10}^5}\text{kWh}$

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

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(B\right)$ is the correct answer.