The table that follows shows some measurementf of the decay rate of a sample of `.^(128)I`, a radio nuclide often used medically as a tracer to measure the rate at which iodine is absorbed by the thyroid gland.
`|{:("Time(min)",A (counts//s),"Time(min)",A(counts)//s,),(4,392.2,132,10.9,),(36,161.4,164,4.56,),(68,65.5,196,1.86,),(10,26.8,218,1.00,):}|`

The half life `t_(1//2)` for this radio nuclide.

Options

A. `25 min`
B. `50 min`
C. `2.5 min`
D. `5 min`

Answer

A

Explanation

`A=A_(0)e^(-lambda t)rArrlnA=lnA_(0)-lambda t`
`:. lambda=(lnA_(0)-lnA)/(t)=(6.2-0)/(225)=0.0275 min^(-1)`
`:. T_(1//2)=(0.693)/(lambda)=25 min`