Question

The Sun has a mass of 2 x 10³⁰ kg and a luminosity of 4 x 10²⁶ W. If we assume that the Sun is comprised entirely of hydrogen nuclei (with a mass of 1.6725 x 10^-27 kg) and all of these nuclei are fused into helium nuclei via the "p-p chain", how long (in years) will it take the Sun to fuse all of its hydrogen into helium?

100 million years

1 billion years

7 billion years

100 billion years

Answer 1

100 billian years

4 protons form 1 He nucleus.

no of protons on the sun, N = 2*10^30/(1.67*10^-27)

= 1.1977*10^57

no of chanin reactions take place = N/4

total amount of energy released, E = (N/4)*26.97 MeV

= (1.1977*10^57/4)*26.97*10^6*1.6*10^-19

= 1.292*10^45 J

the amount time the sun can radiate energy, t = E/P

= 1.292*10^45/(4*10^26)

= 3.23*10^18 s

= 3.23*10^18/(365*24*60*60) years

= 1.024*10^11 years

= 100*10^9 years (when rounded)

= 100 billion years