First slide

Radio activity

Question

The rate of radioactive disintegration at an instant for a radioactive sample of half life $2.2 \times 10^{9} s is 10^{10} s^{- 1}$ The number of radioactive atoms in that sample at that instant is,

Difficult

A

$3.17 \times 10^{19}$
B

$3.17 \times 10^{20}$
C

$3.17 \times 10^{17}$
D

$3.17 \times 10^{18}$

Solution

$T_{1 / 2} = \frac{\ln 2}{λ} = \frac{0.693}{λ} 2.2 \times 10^{9} = \frac{0.693}{λ} λ = \frac{0.693}{2.2 \times 10^{9}} = 3.15 \times 10^{- 10} \begin{array}{l} R = λN & (R is activity) \end{array} N = \frac{R}{λ} = \frac{10^{10}}{3.15 \times 10^{- 10}} = 3.17 \times 10^{19}$

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