In nature, a decay chain series starts with 90 Th 232 and finally terminates at 82 Pb 208 . A thorium ore sample was found to contain 8 × 10 –5 mL of helium at STP and 5 × 10 –7 g of Th 232 . Find the age of the ore sample assuming the source of helium to be only to the decay of Th 232 . Also assume complete retention of helium within the ore (Half life of Th 232 = 1.39 × 10 10 years).
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
Sol. No. of helium atoms in 8 × 10 –5 mL,
= 2.15 × 10 –15 atoms
Now, Th 232 decays to Pb 208 and in the process give six helium atoms.
∴ 232 = 208 + 6 × 4
∴ No. of Th 232 atoms used up to give 8 × 10 –5 mL
Helium
= 
= 3.585 × 10 14 atoms of The
Also, No. of Th 232 atoms left undecayed,
N = 
= 1.298 × 10 15 atoms
∴ No. of Th 232 atoms at start of decay,
N 0 = 3.585 × 10 14 + 1.298 × 10 15 atoms
= 1.6565 × 10 15 atoms
Now, λ = 
= 
= 4.986 × 10 –11 per year
Age of the ore, t = 
log 10 
= 
log 10 
= 
log 10 
= 
log 10 1.2762
4.89 × 10 9 s = 154.26 years
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