Question

A radioactive isotope has a half life of 5 years. How long it will take the activity to reduce to 1.56%

Answer 1

A radioactive isotope has a half life of 5 years.

To find : Time taken the radioactive to reduce to 1.56 %

solution : we know, radioactive reaction is a First order reaction and relation between time and amount of substance is given by,

t = 2.303/λ log [R₀/R]

here, R = 1.56 % of R₀ = 1.56R₀/100 = 0.0156R₀

now, t = 2.303/λ log(1/0.0156) .......(1)

given half life, T½ = 5 years

we know, T½ = ln2/λ

⇒5 = ln2/λ

⇒λ = ln2/5 = 0.1386

putting it equation (1) we get,

t = 2.303/0.1386 log(64.1)

≈ 30 years

Therefore the time taken the radioactive to reduce to 1.56 % is 30 years.