Question

a radioisotope has a half life of three hours how much of a 120g sample remains after 9 hours. what will the g amount be after 3 hours, after 6 hours, and after 9 hours?

Answer 1

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60g after 3 hours, 30g after 6 hours and 15g after 9 hours

Explanation:

Weight of the radioactive sample = 120g

half life time period = 3 hours

(a) The weight of sample after 3 hours

$\textsf{ No. of half lives} = \sf \cancel\frac{3}{3} = 1$

The fraction of sample left

$\sf { \frac{1}{2} }^{1} = \frac{1}{2}$

Mass of the sample left

$\sf \frac{1}{2} \times 120 = \cancel\frac{120}{2} = 60g$

60g of sample is left after 3 hours

(b) The weight of sample after 6 hours

$\textsf{ No. of half lives} = \sf \cancel\frac{6}{3} = 2$

The fraction of the sample left

$\sf { \frac{1}{2} }^{2} = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4}$

Mass of the sample left

$\sf \frac{1}{4} \times 120 = \cancel\frac{120}{4} = 30g$

30g of sample is left after 6 hours

(c) The weight of sample after 9 hours

$\textsf {No. of half lives} = \sf \cancel\frac{9}{3} = 3$

The fraction of sample left

$\sf { \frac{1}{2} }^{3} = \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} = \frac{1}{8}$

Mass of sample left

$\sf \frac{1}{8} \times 120 = \cancel \frac{120}{8} = 15g$

15g of sample is left after 9 hours.