Biologically useful technetium nuclei (with atomic weight 99) have a half life of 6 hrs. A solution containing `10^(-12)` g of this is injected into the bladder of a patient. Find its activity in the beginning and after one hour.

Answer

`7.026xx10^(8)hr^(-1); 6.26xx10^(8)hr^(-1)`

Explanation

Here, `T=6hrs., lambda=0.693/T=0.693/6 hr^(-1)`
No. of atoms in `10^(-12)g` at t=0
`N_(0)=(6.023xx10^(23))/99xx10^(-12)=6.08xx10^(9)`
Activity of the sample at t=0
`((dN)/(dt))_(0)=lambda N_(0)=0.693/6xx6.08xx10^(9)hr^(-1)`
`=7.026xx10^(8)hr^(-1)`
form `N/(N_(0))=(1/2)^(t//T)=(1/2)^(1//6)`
calculate `N=5.423xx10^(9)`
`:. ((dN)/(dt))_(t)=lambdaN=0.693/6xx5.423xx10^(9)`
`=6.26xx10^(8)hr^(-1)`