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A pieces of bone an animals from a ruin is found to have ^{14}

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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)

1672 years

2391 years

3291 years

4453 years

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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

t_{1/2}

=5760 years)

5 mins ago

Discuss this question LIVE

5 mins ago

Text solutionVerified

The initial activity of

c - 12

= 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 ( - )}{ln _{2}} ln (\frac{12}{16}) = lo g_{2} (\frac{3}{4})

So,

t = 5760 lo g_{2} (\frac{4}{3}) ≃ 2390.6 years. (Ans)

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Question Text	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)
Topic	Nuclei
Subject	Physics
Class	Class 12
Answer Type	Text solution:1
Upvotes	97

Text solutionVerified

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A pieces of bone an animals from a ruin is found to have 14C activity of 12 disintegrations per minute per gm of its carbon content. The14C 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 14Cis t1/2​=5760 years)

Text solutionVerified

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