First slide

Radio activity

Question

In moon rock sample the ratio of the number of stable argon-40 atoms present to the number of radioactive potassium-40 atoms is 7:1. Assume that all the argon atoms were produced by the decay of potassium atoms, with a half-life of 2.5 × 10⁹yr. The age of the rock is

Moderate

A

2.5 10⁹ yr
B

5.0 10⁹ yr
C

7.5 10⁹ yr
D

10¹⁰ yr

Solution

At present ; $\frac{No . of \arg on atoms}{No . of K atoms} = \frac{7}{1}$
$\begin{array}{rcl} ∴ \frac{No . of K atoms}{Total No . of atoms} & = & \frac{1}{1 + 7} = \frac{1}{8} = \frac{1}{2^{3}} \\ ∴ \frac{N}{N_{0}} & = & \frac{1}{2^{3}} = \frac{1}{2^{t / T}}; ∴ 3 = t / T \\ t & = & 3 T = 3 x 2.5 x 10^{9}; ∴ t = 7.5 x 10^{9} yr \end{array}$

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