KCET · Physics · Nuclear Physics
The amount of energy released when one microgram of matter is annihilated is
- A \(25 \mathrm{kWh}\)
- B \(9 \times 10^{10} \mathrm{kWh}\)
- C \(3 \times 10^{10} \mathrm{kWh}\)
- D \(0.5 \times 10^{5} \mathrm{kWh}\)
Answer & Solution
Correct Answer
(A) \(25 \mathrm{kWh}\)
Step-by-step Solution
Detailed explanation
According to Einstein's mass energy equivalence relation
\(\begin{aligned}
E &=\mathrm{mc}^{2} \\
&=10^{-6} \times 10^{-3} \times\left(3 \times 10^{8}\right)^{2} \mathrm{~J} \\
&=9 \times 10^{7} \mathrm{~J} \\
&=\frac{9 \times 10^{7}}{3.6 \times 10^{6}} \mathrm{kWh} \\
&=25 \mathrm{kWh}
\end{aligned}\)
\(\begin{aligned}
E &=\mathrm{mc}^{2} \\
&=10^{-6} \times 10^{-3} \times\left(3 \times 10^{8}\right)^{2} \mathrm{~J} \\
&=9 \times 10^{7} \mathrm{~J} \\
&=\frac{9 \times 10^{7}}{3.6 \times 10^{6}} \mathrm{kWh} \\
&=25 \mathrm{kWh}
\end{aligned}\)
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