First slide

Radio activity

Question

The rate of radioactive disintegration at an instant for a radioactive same of half life 2.2 × 10⁹ s is 10¹⁰ s^–1. The number of radioactive atoms in that sample at that instant is,

Moderate

A

3.17 x 10²⁰
B

3.17 x 10¹⁷
C

3.17 x 10¹⁸
D

3.17 x 10¹⁹

Solution

$\begin{array}{rcl} \frac{dN}{dt} & = & λN; \\ \frac{dN}{dt} & = & (\frac{0.693}{T_{1 / 2}}) N \end{array}$
$\begin{array}{rcl} 10^{10} & = & \frac{0.693}{2.2 \times 10^{9}} N \\ N & = & 3.17 \times 10^{19} \end{array}$

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