First slide

Radio activity

Question

Nuclei of a radio active element are produced at the rate of $α = 200 s^{- 1}$ . Initial number of active nuclei of the sample is 4000. It after one half life, rate of disintegration is equal to rate of production, then half life of the radio active element is

Moderate

A

7 sec
B

120 sec
C

200 sec
D

15 sec

Solution

After time t, number of active nuclei is given by $N = N_{0} / {(2)}^{\frac{t}{T}}$
Now rate of disintegration $= λN$
$∴ λN = α \Rightarrow (\frac{\ln 2}{T}) \frac{N_{0}}{{(2)}^{\frac{T}{T}}} = α$
$\Rightarrow T = \frac{N_{0} \ln 2}{2 α} = \frac{4000 \times 0 .693}{2 \times 200} \sec$
$\Rightarrow T = 6 .93 \sec ≃ 7 \sec$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App