Assume the Sun consists entirely of hydrogen and releases 26 MeV in the reaction 4(¹₁H) → ⁴₂He. If the solar power remains 3.9 × 10²⁶ W and the Sun's mass is 1.7 × 10³⁰ kg, the burn time is (8/3) × 10ⁿ s. Find n.
Physics · Nuclear physics
JEE Mains Practice

Question

Assume the Sun consists entirely of hydrogen and releases 26 MeV in the reaction 4(¹₁H) → ⁴₂He. If the solar power remains 3.9 × 10²⁶ W and the Sun's mass is 1.7 × 10³⁰ kg, the burn time is (8/3) × 10ⁿ s. Find n.

Physics · Nuclear physics

G1 Physics · Accepted Answer

Each fusion of four ¹₁H nuclei into ⁴₂He releases 26 MeV = 4.16 × 10⁻¹² J. The number of hydrogen nuclei in the Sun is approximately the Sun's mass divided by the proton mass. Dividing this by 4 gives the total number of possible fusion reactions. Total available fusion energy divided by 3.9 × 10²⁶ W gives a burn time of order (8/3) × 10¹⁸ s. Hence n = 18.