Question

$(-\frac{dN}{dt}=\lambda N)$ represents the rate of decay in disintegration of atoms per unit time, where N is the number of atoms disintegrating at that time and $\lambda$ the disintegration constant. Calculate number of curies when number of atoms equal to one Avogadro's number disintegrates in the case when $\lambda =0.6146\times {10}^{-10}{s}^{-1}$?

• A. 1000 Ci
• B. 300 Ci
• C. 500 Ci
• D. None of these

Answer 1

The correct option is A 1000 Ci

As we know, $(-\frac{dN}{dt}=\lambda N)$

Here as given,

$\lambda =0.6146\times {10}^{-10}$

$N=N_o=6.023\times {10}^{23}$

so

$-\frac{dN}{dt}=0.6146\times 6.023\times {10}^{13}=3.71\times {10}^{13}=1000Ci$

as $1Ci=3.7\times {10}^{10}$ decays per second.