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)

(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,

$A=A_{0}e_{−λt}$

where $λ =Tln_{2} ,$ T = Half life

$⇒12=16e_{−λt}$

$⇒t=ln_{2}T(−) ln(1612 )=Tlog_{2}(43 )$

So,

$t=5760log_{2}(34 )≃2390.6years.$ (Ans)

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