Question

A radioactive sample S₁​ having the activity A₁​ has twice the number of nuclei as another sample S_2​ of activity A₂​ If A₂​ = 2A_1​ then the ratio of half-life of S_1​ to the half-life of S₂​ is ______.

विकल्प

• 0.25

• 0.75

• 4

• 2

Answer 1

A radioactive sample S₁​ having the activity A₁​ has twice the number of nuclei as another sample S_2​ of activity A₂​ If A₂​ = 2A_1​ then the ratio of half-life of S_1​ to the half-life of S₂​ is 4.

Explanation:

Activity, A = λN = `0.693/("T"_1//2)"N"`

Where T_1/2 is the half-life of a radioactive sample

∴ `"A"_1/"A"_2="N"_1/"T"_1xx"T"_2/"N"_2`

 `"T"_1/"T"_2="A"_2/"A"_1xx"N"_1/"N"_2`

= `(2"A"_1)/"A"_1xx(2"N"_2)/"N"_2`

= `4/1`