Question

How much energy is produced, if 2 kg of a substance is fully converted into energy?

• A. \( 3 \times 10^{15} \) J
• B. \( 1.5 \times 10^{16} \) J
• C. \( 3 \times 10^{16} \) J
• D. \( 1.5 \times 10^{14} \) J

Hint:

The equation \( E = mc^2 \) shows how a small amount of mass can be converted into a large amount of energy.

Answer 1

The Correct Option is D

Step 1: Use the energy-mass equivalence relation. The energy produced by converting a mass into energy is given by Einstein’s equation: \[ E = mc^2 \] Where \( m = 2 \, \text{kg} \) and \( c = 3 \times 10^8 \, \text{m/s} \).
Step 2: Substitute the values: \[ E = 2 \times (3 \times 10^8)^2 = 1.5 \times 10^{16} \, \text{J} \]