The table that follows shows some measurements 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 ^(- lamda t) implies ln A = ln A _(0) - lamda t`
`therefore lamda = (ln A _(0) - ln A)/(t) = (6.2 -0)/(225) = 0.0275min ^(-1)`
`therefore T _(1//2)= (0.693)/(lamda ) = 25` min