Question

a) Prove that the mean lifetime of deuteron in the sun's core is 1 second

b) compare the mean lifetime of deuteron and mean lifetime of proton in the sun's core

Answer 1

We know that,

Where m- mass of atom

n - number density

R- total density

We know that

Where

mean molecular weight

Thus for photosphere, we have

Let us aasass the core of the sun is entirely composed of hydrogen during its formation. Thus at the time, the mean molecular mass at the core will be 2 as X =1 at that time.

When half of its hydrogen is deployed, then they are converted in helium. Thus X=0.5, Y=0.5 Z =0(say)

Thus, mean molecular weight at that time

When the hydrogen is completely deployed, then we will have a degenerate helium core. Thus, X=0, Y=1

Then