First slide

Radio activity

Question

At any instant the ratio of the amount of radioactive substances is 2 : 1. If their half-lives be respectively 12 and 16 hours, then after two days, what will be the ratio of the substances?

Moderate

A

1 : 1
B

2 : 1
C

1 : 2
D

1 : 4

Solution

Number of half-lives in two days four substance 1 and 2 respectively are $n_{1} = \frac{2 x 24}{12} = 4 and n_{2} = \frac{2 x 24}{1.6} = 3$
By using $N = N_{0} {(\frac{1}{2})}^{n} \Rightarrow \frac{N_{1}}{N_{2}} = \frac{{(N_{0})}_{1}}{{(N_{0})}_{2}} x \frac{{(\frac{1}{2})}^{n_{1}}}{{(\frac{1}{2})}^{n_{2}}} = \frac{2}{1} x \frac{{(\frac{1}{2})}^{4}}{{(\frac{1}{2})}^{3}} = \frac{1}{1}$

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