The energy equivalent of 1 g of substance is :

Solution

Physics sir · 4 steps

Use E = mc² with mass in kilograms, then convert joules to MeV.

1. Mass in SI units. Take m = 1 g = 10⁻³ kg and c = 3 × 10⁸ m s⁻¹.

   E = mc² = 10⁻³ × (3 × 10⁸)² = 9 × 10¹³ J

2. Convert to MeV. 1 MeV = 1.6 × 10⁻¹³ J, so E = (9 × 10¹³)/(1.6 × 10⁻¹³) = 5.6 × 10²⁶ MeV.
3. Cross-check. 1 g holds 6.02 × 10²³ atomic mass units, and each is worth 931.5 MeV. The product is 6.02 × 10²³ × 931.5 ≈ 5.6 × 10²⁶ MeV, the same answer.
4. So. The energy equivalent of 1 g is about 5.6 × 10²⁶ MeV, which is option (a).

The idea to keep. For mass-energy questions, put mass in kg in E = mc² and keep 1 MeV = 1.6 × 10⁻¹³ J handy. Using 1 u = 931.5 MeV is a quick way to check the answer.

Answer from the NTA final answer key. Solution by PrepWiser.