Nuclear Physics And Radioactivity Question 54
Question: A star initially has $ 10^{40} $ deuterons. It produces energy via the processes $ _{1}H^{2}+ _{1}H^{2}\to _{1}H^{3}+p $ $ _{1}H^{2}+ _{1}H^{3}\to _{2}He^{4}+n $ The masses of the nuclei are as follows : $ M(H^{2})=2.014\ amu;\ M(p)=1.007\ amu; $ $ M(n)=1.008\ amu;\ M(He^{4})=4.001\ amu $ If the average power radiated by the star is $ 10^{16}W $ ,the deuteron supply of the star is exhausted in a time of the order of [IIT 1993]
Options:
A) $ 10^{6} $ sec
B) $ 10^{8} $ sec
C) $ 10^{12} $ sec
D) $ 10^{16} $ sec
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Answer:
Correct Answer: C
Solution:
Mass defect = $ RV\propto n $ $ =0.026\ amu=0.026\times 931\times 10^{6}\times 1.6\times {{10}^{-19}}J $ $ =3.82\times {{10}^{-12}}J $ Power of star =1016W Number of deuterons used $ =\frac{10^{16}}{\Delta M}=0.26\times 10^{28} $ Deuteron supply exhausts in $ \frac{10^{40}}{0.26\times 10^{28}}=10^{12}s $ .
BETA
