Name: Uses of Radiation
Uploaded: 2019-07-19
Duration: 4 min 53 s
Description: This video discusses the various applications of radiation in the field of medicine to treat cancer, thyroid glands etc. Watch this to know more.

Question

What is meant by the activity of a radioactive substance?

Draw time-activity graph for a radioactive substance. Find the activity after four half-lives in terms of initial activity After how much time the activity will become zero?

Accepted Answer

The rate of decay of a radioactive substance is called the activity of the substance.

$R = \frac{- d N}{d t}$

Suppose $N$ is the size of a population of radioactive atoms at a given time $t$ and $N_{0}$ is the population of initial radioactive atoms at $t = 0$ .

According to Rutherford and Soody law, $\frac{- d N}{d t} \propto N$

$∴ R \propto N$

The time required for half of the original population of radioactive atoms to decay is called Half-life.

At $t = t_{\frac{1}{2}}$ , $N = \frac{N_{0}}{2}$

$\Rightarrow N = N_{0} {(\frac{1}{2})}^{1}$

After two half lives, $N = N_{0} {(\frac{1}{2})}^{2}$ and so on....

After $n$ half lives, $N = N_{0} {(\frac{1}{2})}^{n}$

Graph between un disintegrated atoms of the element and time is drawn below.

After four half lives, $N = N_{0} {(\frac{1}{2})}^{4} = \frac{N_{0}}{16}$

Activity will be zero only after infinite time. This means it will never become zero.

What is meant by the activity of a radioactive substance?

Draw time-activity graph for a radioactive substance. Find the activity after four half-lives in terms of initial activity After how much time the activity will become zero?

Important Questions on Radioactivity

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