The disintegration rate of a certain in radioactive sample at an instant is 4750 dpm. 10 minutes later the rate becomes 2760 dpm. What is the half-life of sample.

Options

A. 12.8 min
B. 11.2 min
C. 14.2 min
D. 6.8 min

Answer

A

Explanation

Given `N_(0) = 4750` dpm, N = 2760 dpm, t = 10 min, `t_(0.5) = ?`
`lambda = (2.303)/(t) log "" (N_(0))/(N) = (2.303)/(10) log "" (2.303)/(10) log "" (4750)/(2760) = 5.4 xx 10^(-2) min^(-1) " "therefore t_(0.5) = (0.693)/(lambda) = (0.693)/(5.4 xx 10^(-2)) = 12.8` min