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Question

Before 1900, the activity per mass of atmosphere carbon due to the presence of 14C averaged about 0.255 Bq per gram of C. What fraction of carbon atoms were 14C?
Given: Half life is 5730 years.

  1. One 14C in every 3×1012 atoms
  2. Four 14C in every 1010 atoms
  3. Three 14C in every 1012 atoms
  4. Two 14C in every 1011 atoms

A
One 14C in every 3×1012 atoms
B
Four 14C in every 1010 atoms
C
Two 14C in every 1011 atoms
D
Three 14C in every 1012 atoms
Solution
Verified by Toppr

Decay constant, λ=ln2t1/2=1.209×104yr1
Activity is given by: dNdt=λN
Hence, N=dN/dtλ=6.66×1010
Number of carbon atoms in 1 gm is 6×102312=5×1022
Fraction of 14C is given by:
6.66×10105×1022=1.33×1012

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Before 1900, the activity per mass of atmosphere carbon due to the presence of 14C averaged about 0.255 Bq per gram of C. What fraction of carbon atoms were 14C?
Given: Half life is 5730 years.

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