The ratio of C14 to C12 in a living matter is measured to be \frac{C^{14}}{C^{12}}= 1.3 × 10–12 at the present time. Activity of 12.0 g carbon sample is 180 dpm. The half life of C14 is nearly ____

Engineering

Chemistry

Kinetics of Radioactive Decay

Question

The ratio of C¹⁴ to C¹² in a living matter is measured to be $\frac{C^{14}}{C^{12}}$ = 1.3 × 10^–12 at the present time. Activity of 12.0 g carbon sample is 180 dpm. The half life of C¹⁴ is nearly _____ × 10¹² sec.

[Given : N_A = 6 × 10²³]

1.8

0.384

0.18

648

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$n_{C} = \frac{12}{12} = 1$

$n_{C^{14}}$ = 1.3 × 10^–12 (approximately)
atoms of C¹⁴ = 1.3 × 10^–12 × 6 × 10²³ ⇒ 7.8 × 10¹¹
A = $\frac{180}{60}$ decay/sec. = λ (7.8 × 10¹¹) ; $λ = \frac{3}{7 .8 \times 10^{11}}$
$= \frac{30}{7 .8} \times 10^{- 12} \Rightarrow 3 .846 \times 10^{- 12}$ ; $t_{1 / 2} = \frac{0 .693}{λ} = 0 .18 \times 10^{12} \sec .$