The energy equivalent of 1 g of a substance in joules is:
Show Hint
- \( 9 \times 10^{13} \)
- \( 4.5 \times 10^{13} \)
- \( 1 \times 10^{13} \)
- \( 0.5 \times 10^{13} \)
- \( 2.25 \times 10^{13} \)
The Correct Option is A
Solution and Explanation
Step 1: The energy equivalent \( E \) of mass \( m \) is given by Einstein's equation: \[ E = mc^2 \]
where:
- \( m = 1 \, {g} = 1 \times 10^{-3} \, {kg} \),
- \( c = 3 \times 10^8 \, {m/s} \).
Step 2: Substitute the values into the equation: \[ E = (1 \times 10^{-3}) \times (3 \times 10^8)^2 = 9 \times 10^{13} \, {J} \]
Thus, the energy equivalent of 1 g of substance is \( 9 \times 10^{13} \, {J} \).
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