Question

28.
A radioactive sample disintegrates by 10% during
one month. How much fraction will disintegrate
four months :-
(1) 34.39%
(2) 40%
(3) 38%
(4) 50%​

Answer 1

Thus, the amount of disintegrated part is 34.39%.

Step by step explanation:

N = No - 10 % of No = 90% of No

time taken,  = 1 month

Let λ be the disintegration constant.

So use the equation of radioactivity

$N=N_{0}e^{-\lambda t}$

$0.9=e^{-\lambda \times 1}$  

Taking natural log on both the sides

ln (0.9) = - λ

λ = 0.1054 per month

Let the remaining percentage after 4 months be y.

$y=e^{-\lambda \times 4}$  

Substitute the value of λ

$y=e^{- 0.1054 \times 4}$  

$y=e^{-0.4214}$  

Taking natural log on both the sides

ln y = - 0.4214

y = 0.656 = 65.6 %

The amount which is disintegrated is 100 - 65.6 = 34.39%

Thus, the amount of disintegrated part is 34.39%.