Determine the mass of `Na^(22)` which has an activity of 5mCi. Half life of `NA^(22)` is 2.6 years. Avogadro number `=6.023xx10^(23)` atoms.

Explanation

Activity of `Na-22`
`A= (dn)/(dt) = 5mc`
`A =5xx10^(-3)xx3.7xx10^(10)`
`A=1.85xx10^(7)` disintegration /second
Distegration constant `lamda= (0.693) /(T) = (0.693)/(2.6xx365xx24xx60xx60)`
`lamda= 8.453xx10^(-9)S^(-1)`
Activity `(dN)/(dt) = lamdaN`
`N= (1)/(lamda) (dN)/(dt)`
`N= (1)/(8.453xx10^(-9))xx1.85xx10^(7)`
`N= 2.189xx10^(160)`atoms
According to Avagadro .s hypothesis
`6.0223xx10^(23)` atoms of `Na - 22 weight 22gm2.189xx10^(16)` atoms weight
`mass = 922xx10^(-3)/(6.023xx10^(23) xx2.189xx10^(16)`
mass `= 7.996xx10^(10)kg`