(a) Calculate the activity of one mg sample `._(28^(Sr^(90)))` whose half life period is `28` years.
(b) An experiment is performed to determine the half-life of a radioactive substance which emits one beta particle for each decay process. Observation shown that an average of `8.4 beta-`particles are emitted each second by `2.5 mg` of the substance. the atomic weight of the substance is `230`. calculate the half0life of the substance.
(c) Determine the quantity of `._(84^(Po^(210)))` necessary to provide a source of alpha particle of `5mCi` strength (`T_(1//2)` for Po `= 138` day).

Explanation

(i) number of atoms `,N=("Mass")/("Atomic weight"xxN_(A),`
(where `N_(A)` is Avogadro number )
`=(2xx10^(-3))/(90)xx6.023xx10^(23)`
`=13.38x10^(18)`
Decay constant ,` lamda =("in "2)/(T_(1//2))=(0.693)/(287)//yr`
Activity ,`R=lamda N=(0.693)/(28)xx13.38xx10^(18)`
`=0.331xx10^(18)//yr`
`=(0.331xx10^(18))/(365xx24xx3600)=10^(10)`dps
(ii) Half -life of the substance
`N=(2.5xx10^(-3))/(230)xx6.023xx10^(23)=6.5xx10^(18)`
Activity `,R=8.4//s =lamda N =("in2")/(T_(1//2))Nimplies T_(1//2)=("in2")/(A)N` ,
half -life of the substance
`T_(1//2)=(0.693xx6.5xx10^(18))/(8.4)`
`=0.54xx10^(18)s=1.7xx10^(10)yr`