First slide

Radio activity

Question

The rate of disintegration was observed to be $10^{17}$ disintegrations per sec when its half life period is 1445 years.
The original number of particles are

Difficult

A

$8.9 x 10^{27}$
B

$6.6 x 10^{27}$
C

$1.4 x 10^{16}$
D

$1.2 x 10^{17}$

Solution

Rate of disintegration $\frac{dN}{dt} = 10^{17} s^{- 1}$
Half life $T_{1 / 2} = 1445 year$
$= 1445 x 365 x 24 x 60 x 60 = 4.55 x 10^{10} \sec$
Now decay constant
$λ = \frac{0.693}{T_{1 / 2}} = \frac{0.93}{4.55 x 10^{10}} = 1.5 x 10^{- 11} per \sec$
The rate of disintegration
$\frac{dN}{dt} = λ x N_{0} \Rightarrow 10^{17} = 1.5 x 10^{- 11} x N_{0} \Rightarrow N_{0} = 6.6 x 10^{27} .$

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