The radio isotope `""_(15)^(32)P` is used to bio-chemical studies. A sample containing this isotope has an activity 1000 times the detectable limit. How long could an experiment be run with the sample before the radioactivity could no longer be detected ? Half-life of `""_(15)^(32)P` is 14.2 days.

Options

A. 141.5 days
B. 145.5 days
C. 143.5 days
D. 148.5 days

Answer

A

Explanation

`(N_(0))/(N) = (1000)/(1)`
`lambda = (2.303)/(t) log "" (N_(0))/(N) or t = (2.303)/(lambda ) log "" (N_(0))/(N) = (2.303)/((0.693//(14.2)) log "" (1000)/(1) = 141.5` days