Question:
How much energy is produced, if 2 kg of a substance is fully converted into energy?
How much energy is produced, if 2 kg of a substance is fully converted into energy?
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The equation \( E = mc^2 \) shows how a small amount of mass can be converted into a large amount of energy.
Updated On: Apr 28, 2026
- \( 3 \times 10^{15} \) J
- \( 1.5 \times 10^{16} \) J
- \( 3 \times 10^{16} \) J
- \( 1.5 \times 10^{14} \) J
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The Correct Option is D
Solution and Explanation
Step 1: Apply Einstein’s mass-energy equivalence
The energy released when mass is converted into energy is given by Einstein’s relation:
\(E = mc^2\)
Here, \(m = 2\ \text{kg}\), \(c = 3 \times 10^8\ \text{m/s}\)
Step 2: Substitute the values
\[ E = 2 \times (3 \times 10^8)^2 \] \[ E = 2 \times 9 \times 10^{16} \] \[ E = 1.8 \times 10^{17}\ \text{J} \]
Final Answer:
\(E = 1.8 \times 10^{17}\ \text{J}\)
The energy released when mass is converted into energy is given by Einstein’s relation:
\(E = mc^2\)
Here, \(m = 2\ \text{kg}\), \(c = 3 \times 10^8\ \text{m/s}\)
Step 2: Substitute the values
\[ E = 2 \times (3 \times 10^8)^2 \] \[ E = 2 \times 9 \times 10^{16} \] \[ E = 1.8 \times 10^{17}\ \text{J} \]
Final Answer:
\(E = 1.8 \times 10^{17}\ \text{J}\)
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