Question

The energy equivalent of 1.0 kg of substance is ______.

• A. $9 \times 10^{13}$ J
• B. $3 \times 10^{13}$ J
• C. $9 \times 10^{16}$ J
• D. $9 \times 10^{14}$ J

Hint:

$1\text{ kg}$ of matter contains a \textbf{staggering} amount of energy—enough to power a large city for quite some time if it could be converted perfectly!

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Mass and energy are interconvertible according to Einstein's mass-energy equivalence relation.
Step 2: Calculation:
Formula: $E = mc^2$ Given: $m = 1.0\text{ kg}$, $c = 3 \times 10^8\text{ m/s}$. $$E = 1.0 \times (3 \times 10^8)^2$$ $$E = 1.0 \times 9 \times 10^{16}$$ $$E = 9 \times 10^{16}\text{ J}$$
Step 3: Final Answer:
The energy equivalent is $9 \times 10^{16}$ J.