(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

Given that activity = `8.4 sec^(-1)`
According to Avogadro's hypothesis, the number of atoms in 2.5 mg
`N=(6.02xx10^(23))/(230)xx2.5xx10^(16)`
Now `lambdaN=8.4sec^(-1)`
`therefore` `lambda=(8.4)/(N)= (8.4)/( 6.54xx10^(18))=1.28xx10^(-18)sec^(-1)` `therefore` `T=(0.6931)/(lambda)=(0.6931)/(1.28xx10^(-18))sec=1.71xx10^(10)`years