The activity of a radioactive sample is measured as `9750` counts per minute at `t = 0` and as `975` counts per minute at `t = 5` minutes. The decay constant is approximately

Options

A. 0.92 per minute
B. 0.23 per minute
C. 0.69 per minute
D. 0.46 per minute

Answer

D

Explanation

`A = A_0 e^(-lamdat)`
`therefore 975 = 9750 e^(-5lamda)`
`975/9750 = 1/10 = (1)/(e^(5lamda))`
`therefore e^(5lamda) = 10 " or " 5 lamda = log_e 10 = 2.3026 log_(10) 10 = 2.3026`
`therefore lamda = (2.3026)/(5) = 0.46`