Question

A radioactive element is half disintegrated in 40 minutes. What is the time required for the decay of 75% of the element?

Answer 1

Given:

Half-life t_1/2 = 40 minutes

We need to find time for 75% decay, i.e., when 25% remains

For a first-order reaction use 

`t = 2.303/k log ([A]_0/([A]))`

= `2.303/k log (1/(1 - x))`

Where x = 0.75 (i.e., 75% decay)

∴ `k = 0.693/t_(1//2)`

= `0.693/40`

= 0.017325 min⁻¹

Time for 75% decay

`t = 2.303/0.017325 log (1/0.25)`

= `2.303/0.017325 log (4)`

= `(2.303 xx 0.6021)/0.017325`    ...(log 4 = 0.6021)

= `1.3875/0.017325`

t = 80.1 minutes