(a) A radioactive sample has `6.0 xx 10^(18)` active nuclei at a certain instant. How many of these nuclei will still be the same active state after two half-lives?
(b) Radioactive phosphours`-32` has a half-life of `14` days. A source containing this isotope has an initial activity of `10muCi`.
(i) What is the activity of the source after `42` days?
(ii) What time elapse before the activity of the source falls at `2.5muCi`?
(c) `1g` of a radioactive substance disintergrates at the rate of `3.7 xx 10^(10) dps`. The atomis mass of the substance is `226`. Calculate its mean life.

Explanation

(a) `N = N_(0)((1)/(2))^(n)`
`n = 2`
`N = (N_(0))/(4) = (6xx10^(18))/(4) = 15 xx 10^(17)`
(b) `t = nT_(1//2)`
`42 = nxx14 rArr n = 3`
(i) `A = A_(0) ((1)/(2))^(n) = A_(0)((1)/(2))^(3) = (A_(0))/(8) = (10)/(8) muCi = 1.25muCi`
(ii) `A = A_(0) ((1)/(2))^(n)`
`2.5 = 10((1)/(2))^(n) rArr (1)/(4) = ((1)/(2))^(n)`
`n =2`
`t = nT_(1//2) = 2xx14 = 28` days
(c) `N = (m)/(M) N_(A)`
`A = lambdaN = (1)/(barT)(mN_(A))/(M)`
`bar(T) = (mN_(A))/(MA) = (1xx6.023xx10^(23))/(226xx3.7xx10^(10)) sec`
=` 7.2 xx 10^(10) sec`