Question

Iodine 131 half life is 8.0 days. Ten percent of the original sample o his isotope remains after (a) 22.7 days (b) 24.9 days (c) 26.6 days (d) 28.1 days

Answer 1

option (c) is correct

Step-by-step explanation:

Half life of a substance is the time in which the element becomes half of is initial value.

half life, T = 8 days

Amount remaining, N = 10 % of original value

Let the original value is No.

N = 10% of No

N = 0.1 No

Let the time taken is t and the decay constant is λ.

The relation between the decay constant and the half life is given by

`\lambda =(0.6931)/(T)=(0.6931)/(8)=0.08664 per day`

Us the equation of radioactivity

`N=N_(0)e^(-\lambda t)`

`0.1N_(0)=N_(0)e^(-0.08664 t)`

`e^(0.08664 t)=10`

Taking natural log on both the sides, we get

0.08664 t = 2.303

t = 26.6 days