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Class 12 Physics Modern Physics Nuclei

A pieces of bone an animals from a ruin is found to have

^{14} C

activity of 12 disintegrations per minute per gm of its carbon content. The

^{14} C

activity of of a living animal is 16 disintegration per minute per gm How long ago nearly did the animal die?
(Given half of life

^{14} C

is

t_{1 / 2}

=5760 years)

(a)

1672 years

(b)

2391 years

(c)

3291 years

(d)

4453 years

Correct answer: (b)

Solution:

The initial activity of c -12 is

= A_{0} = 16

dpm.

after a time of t years, activity reduces to A = 12 dpm.

from Radioactivity Law,

A = A_{0} e^{- λ t}

where

λ = \frac{l n _{2}}{T},

T = Half life

\Rightarrow 12 = 16 e^{- λ t}

\Rightarrow t = \frac{T ( - )}{l n _{2}} l n (\frac{1 2}{1 6}) = T l o g_{2} (\frac{3}{4})

So,

t = 5760 l o g_{2} (\frac{4}{3}) ≃ 2390.6 y e a r s .

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