A star has 100% helium composition. It starts to convert three ⁴He into one ¹²C via triple alpha process as
⁴He + ⁴He + ⁴He → ¹²C + Q.
The mass of the star is 2.0 × 10³² kg and it generates energy at the rate of 5.808 × 10³⁰ W. The rate of converting these ⁴He to ¹²C is n × 10⁴² s⁻¹, where n i $s _______.$
[Take, mass of ⁴He = 4.0026 u, mass of ¹²C = 12 u]

Question

A star has 100% helium composition. It starts to convert three ⁴He into one ¹²C via triple alpha process as

⁴He + ⁴He + ⁴He → ¹²C + Q.

The mass of the star is 2.0 × 10³² kg and it generates energy at the rate of 5.808 × 10³⁰ W. The rate of converting these ⁴He to ¹²C is n × 10⁴² s⁻¹, where n i $s _______.$

[Take, mass of ⁴He = 4.0026 u, mass of ¹²C = 12 u]

G1 Physics · Accepted Answer

Energy released per triple-alpha reaction: Δm = 3(4.0026) - 12 = 0.0078 u Using: 1 u c² ≈ 931.5 MeV Q ≈ 0.0078 × 931.5 ≈ 7.27 MeV Convert to joule: Q ≈ 7.27 × 10⁶ × 1.6 × 10⁻¹⁹ J ≈ 1.163 × 10⁻¹² J Reaction rate: N/t = Power/Q = (5.808 × 10³⁰)/(1.163 × 10⁻¹²) ≈ 5 × 10⁴² s⁻¹ Therefore, according to the official NTA key: n = 5