A radioactive material is reduced to `1/16` of its original amount in 4 days. How much material should one begin with so that `4xx10^-3kg` of the material is left over after 6 days ?

Explanation

Given, `N= N_(0)/16`
If n is the number of half-lives, then
`N/N_(0) =(1/2)^(n)`
`rArr 1/16 = (1/2)^(n) rArr n=4`
Given, time of disintegration, t= 4 days
`therefore` Half-life,
`T_(1//2) =t/n = (4 "days")/4 = 1 day`
Given, `N = 4 xx 10^(-3)` kg, t= 6 days
`therefore n=t/T_(1//2) = 6/1 =6`
`therefore N_(0) = N(2)^(n) = 4 xx 10^(-3) xx (2)^(6) = 256 xx 10^(-3) kg`