Atoms And Nuclei Question 388

Question: The ratio of number of atoms of 14C to 12C in living matter is measured to be 1.3×1012 at the present time. A 12 g sample of carbon produces 180 decays/min due to the small amount of 14C in it. The half-life of 14C is nearly [1 year =3.15×107s ]

Options:

A) 574 years

B) 5740 years

C) 2870 years

D) 287 years

Show Answer

Answer:

Correct Answer: B

Solution:

  • 14C12C=1.3×1012

    12g contain 6.022×1023

    atoms No. atoms of 14C=6.022×1023×1.3×1012 =7.8286×1011N=N0eλt

    dNdt=N0eλt×λdNdt=N×λ

    18060=7.8286×1011×λ
    1λ=7.8286×10113λ=0.3832×1011

    t1/2=0691λ=0.6920.3832×1011=1.80×1011sec Half life =1.8032×1011sec=0.5740×104 year=5740 years.



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