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It is known that the ratio of { }^{14} {C} to { }^{12} {C} ato

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Solving time: 3 mins

It is known that the ratio of $^{14} C$ to $^{12} C$ atoms in living beings and atmosphere is a constant. In one experiment it was found that the radiocarbon activity of a living thing is 16 disintegration per minute per gram of carbon content. Find the ratio of $^{14} C$ to $^{12} C$ atoms in your body. Half life of beta decay of $^{14} C$ is $5760 yr = 3.03 \times 1 0^{9}$ minute.

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Problems in Physics II for IIT JEE (McGraw Hill)

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It is known that the ratio of

^{14} C

^{12} C

atoms in living beings and atmosphere is a constant. In one experiment it was found that the radiocarbon activity of a living thing is 16 disintegration per minute per gram of carbon content. Find the ratio of

^{14} C

^{12} C

atoms in your body. Half life of beta decay of

^{14} C

5760 yr = 3.03 \times 1 0^{9}

minute.

6 mins ago

Discuss this question LIVE

6 mins ago

Text solutionVerified

No. of

^{14} C

atom in

1 g

carbon

N = \frac{A}{λ} = \frac{t _{1/2} A}{0.693} = \frac{( 3.03 \times 1 0 ^{9} min ) \times 16}{0.693} = 6.99 \times 1 0^{10}

There are

\frac{1}{12} mol

C

atoms in

1 g

∴

Total no of

C

atoms in

1 g

No = \frac{1}{12} \times 6.02 \times 1 0^{23}

∴

Required ratio

= \frac{6.99 \times 1 0 ^{10}}{\frac{6.02}{12} \times 1 0 ^{23} - 6.99 \times 1 0 ^{10}} ≃ \frac{6.99 \times 1 0 ^{10}}{\frac{6.02}{12} \times 1 0 ^{23}} = 1.37 \times 1 0^{- 12}

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Question Text	It is known that the ratio of $^{14} C$ to $^{12} C$ atoms in living beings and atmosphere is a constant. In one experiment it was found that the radiocarbon activity of a living thing is 16 disintegration per minute per gram of carbon content. Find the ratio of $^{14} C$ to $^{12} C$ atoms in your body. Half life of beta decay of $^{14} C$ is $5760 yr = 3.03 \times 1 0^{9}$ minute.
Topic	Nuclei
Subject	Physics
Class	Class 12
Answer Type	Text solution:1
Upvotes	103

Text solutionVerified

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