Question

The activity of a radioactive substance decreases by a factor of 32 in one hour. The half-life of the substance (in min) is ______.

Options

• 15

• 10

• 20

• 12

Answer 1

The activity of a radioactive substance decreases by a factor of 32 in one hour. The half-life of the substance (in min) is 12.

Explanation:

The activity of a radioactive sample is given by,

`A = A_0(1/2)^{t/T_{1"/"2}}`

⇒ `A/A_0 = (1/2)^{t/T_{1"/"2}}`

Given, `A = A_0/32` and t = 1h

⇒ `(1/32) = (1/2)^{1/T_{1"/"2}}` or `(1/2)^5 = (1/2)^{1/T_{1"/"2}}`

⇒ `5 = 1/T_{1"/"2}`

or `T_{1"/"2} = 1/5h = 60/5` min = 12 min