Question

Weight of $14C$ to have radioactivity $1$ curie is:

(Disintegration constant $=4.4\times {10}^{-12}{sec}^{-1}$)

• A. $2\times {10}^{-4}kg$
• B. $0.9\times {10}^{-4}kg$
• C. $1.7\times {10}^{-4}kg$
• D. $3.7\times {10}^{-10}kg$

Answer 1

Answer: (A)

$2\times {10}^{-4}kg$

$1$ curie $=3.7\times {10}^{10}$ dps

disintegration constant$=4.4\times {10}^{-12}{sec}^{-1}$

$-\frac{dN}{dt}=N\lambda$
$3.7\times {10}^{10}=N\times 4.4\times {10}^{-12}$
$N=8.4\times {10}^{21}=$ Number of $14C$ atoms.

Number of moles of $14C$ $=\frac{8.4\times {10}^{21}}{6.023\times {10}^{23}}=0.0139$

Mass of of $14C$ $=0.0139\times 14=0.195$ g

$=\frac{0.195}{1000}$ kg (as 1 kg $=$ 1000 g)

$=2\times {10}^{-4}$ kg.