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The β - activity of a sample of C O 2 prepared from a contemporary wood gave a count rate of 25.5 counts per minute ( cpm ) . The same mass of C O 2 from an ancient wooden statue gave a count rate of 20.5 cpm under the same conditions. If the half life of 14 C is 5770 years , then the age of the statue is close to [Take log 10 255 205 ≈ 0 . 095 ]

Options

  1. A1822 years
  2. B182   years
  3. C822   years
  4. D18220   years

Correct answer

A. 1822 years

Step-by-step solution

r = 20.5 c p m , r 0 = 25.5 c p m ∵ r 0 ∝ N 0 a n d r ∝ N ∴ r 0 r = N 0 N Also, t = 2 .303 λ log ⁡ N 0 N = 2 .303 λ log ⁡ r 0 r t = 2 .303 × 5770 0 .693 log ⁡ 25 .5 20 .5 = 1822 years

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