First slide

Radio activity

Question

The half life of a radioactive sample undergoing $α$ – decay is $1.4 \times 10^{17}$ s. If the number of nuclei in the sample is $2.0 \times 10^{21}$ ,the activity of the sample is nearly

Moderate

A

$10^{3} Bq$
B

$10^{4} Bq$
C

$10^{5} Bq$
D

$10^{6} Bq$

Solution

The activity (A) is defined as the rate of decay of radioactive substance.
$\begin{array}{l} A = - \frac{dN}{dt} = Nλ \\ A = N \times \frac{0 .693}{T} [T is half life] \\ A = 2 \times 10^{21} \times \frac{0 .693}{1 .4 \times 10^{17}} \\ A = 10^{4} Bq \end{array}$

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