Atomic StructureHard
Question
A star initially has 104 deutetron. It produces energy via the processes
1H2 + 1H2 → 1H3 + p and 1H2 + 1H3 → 2He4 + n.
If the average power radiated by the star is 1016 W, the deuteron supply of the star is exhausted in a time of the order of
The mass of the nuclei are follows
M(H2) = 2.014 amu; M(n) = 1.008amu;
M(p) = 1.007 amu; M(He4) = 4.001 amu.
1H2 + 1H2 → 1H3 + p and 1H2 + 1H3 → 2He4 + n.
If the average power radiated by the star is 1016 W, the deuteron supply of the star is exhausted in a time of the order of
The mass of the nuclei are follows
M(H2) = 2.014 amu; M(n) = 1.008amu;
M(p) = 1.007 amu; M(He4) = 4.001 amu.
Options
A.106s
B.108s
C.1012s
D.1016s
Solution
The given reactions are :
1H2 + 1H2 → 1H3 + p
1H2 + 1H3 → 2He4 + n
3 1H2 → 2He4 + n + p
Mass defect
ᐃm = (3 × 2.014 - 4.001 - 1.007 - 1.008) amu
= 0.026 amu
Energy released = 0.026 × 931 MeV
= 0.026 × 931 × 1.6 × 10-13 J
= 3.87 × 10-12 J
This is the energy produced by the consumption of three deutron atoms.
∴ Total energy released by 1040 deutrons
× 3.87 × 1012 J = 1.29 × 1028 J
The average power radiated is P = 1016 W or 1016 J/s.
Therefore, total time to exhaust all deutrons of the star will be
1.29 × 1012s 
1012s
1H2 + 1H2 → 1H3 + p
1H2 + 1H3 → 2He4 + n
3 1H2 → 2He4 + n + p
Mass defect
ᐃm = (3 × 2.014 - 4.001 - 1.007 - 1.008) amu
= 0.026 amu
Energy released = 0.026 × 931 MeV
= 0.026 × 931 × 1.6 × 10-13 J
= 3.87 × 10-12 J
This is the energy produced by the consumption of three deutron atoms.
∴ Total energy released by 1040 deutrons
× 3.87 × 1012 J = 1.29 × 1028 J The average power radiated is P = 1016 W or 1016 J/s.
Therefore, total time to exhaust all deutrons of the star will be
1.29 × 1012s 1012s Create a free account to view solution
View Solution FreeMore Atomic Structure Questions
In an atom bomb, the energy is released because of the :...The intensity of X-rays from collidge tube is plotted against wavelength λ as shown in the figure. The minimum wave...If the binding energy per nucleon in Li7 and He4 nuclei are respectively 5.60 MeV and 7.06 MeV, then energy of reaction ...freshly prepared radioactive source of half-life 2 h emits radiation of intensity which is 64 times of the permissible s...The volume (V) of a monatomic gas varies with its temperature (T), as shown in the graph. The ratio of work done by the ...