Question

A star initially has 10⁴⁰ deutrons. It produces energy via the process ₁H² + ₁H² + p and ₁H² + ₁H³ → ₂He⁴ + n. If the average power radiated by the star is 1016 W, the deutron supply of the star is exhausted in a time of the order of 

(1) 10⁶ s 

(2) 10⁸ s 

(3) 10¹² s

(4) 10¹⁶ s

Answer 1

Correct option: (3) 10¹²s

Explanation: 

The given reactions are

Mass defect Δm = (3×2.014 – 4.001 – 1.007–1.0008) = 0.026 amu

Energy released = 0.026×931 MeV

= 0.026 × 931 × 1.6 × 10^–13 = 3.87×10^–13 J

This is the energy produced by the consumption of 3 deutron atoms.

The energy released by 10⁴⁰ deutrons 

The average power radiated is 10¹⁶W = 10¹⁶ J/s 

∴ Time required to exhaust all the deutron of the star will be given by