A radioactive element has rate of disintegration `10,000` disintegrations per minute at a particular instant. After four minutes it becomes `2500` disintegrations per minute. The decay constant per minute is

Options

A. `0.2 log_e2`
B. `0.5 log_e2`
C. `0.6 log_e2`
D. `0.8 log_e2`

Answer

B

Explanation

`N = N_0e^(-lamdat)`
`therefore N/N_0 = e^(-lamdat) therefore 2500/10000 = e^(-lamdaxx4)`
`therefore 1/4 = (1)/(e^(4lamda) therefore e^(4lamda) = 4`
`therefore 4 lamda = log_e 4 = log_e (2^2)`
`therefore 4lamda = 2 log_(e) 2`
`therefore lamda = 2/4 log_(e)2`
`therefore lamda = 0.5 log_(e) 2`