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>>Class 12
>>Physics
>>Nuclei
>>First Order Radioactive Decay
>> $Before 1900 , the activity per mass of a$

Question

Before $1900$ , the activity per mass of atmosphere carbon due to the presence of $^{14} C$ averaged about $0.255 B q$ per gram of $C$ . What fraction of carbon atoms were $^{14} C$ ?
Given: Half life is $5730$ years.

A

One $^{14} C$ in every $3 \times 1 0^{12}$ atoms

B

Three $^{14} C$ in every $1 0^{12}$ atoms

C

Four $^{14} C$ in every $1 0^{10}$ atoms

D

Two $^{14} C$ in every $1 0^{11}$ atoms

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Updated on : 2022-09-05

Solution

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Correct option is A)

Decay constant, $λ = \frac{l n 2}{t _{1 / 2}} = 1.209 \times 1 0^{- 4} y r^{- 1}$
Activity is given by: $\frac{d N}{d t} = λ N$
Hence, $N = \frac{d N / d t}{λ} = 6.66 \times 1 0^{10}$
Number of carbon atoms in 1 gm is $\frac{6 \times 1 0 ^{23}}{1 2} = 5 \times 1 0^{22}$
Fraction of $^{14} C$ is given by:
$\frac{6 . 6 6 \times 1 0 ^{10}}{5 \times 1 0 ^{22}} = 1.33 \times 1 0^{- 12}$

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