Define ‘disintegration constant’ and ‘mean life’ of a radioactive substance. Give the unit of each.

Explanation

Disintegration or decay constant : According to law of radioactive decay the instantaneous rate of disintegration `(-(dN)/(dt))` of a radioactive element is directly proportional to the actual number of nuclides of that element present at that instant i.e., `-(dN)/(dt)=lambdaN`, where `lambda` is the disintegration constant. Hence, disintegration constant of a radioactive substance is defined as the ratio of its instantaneous rate of disintegration to the number of nuclides present at that time. Its SI unit is `s^(-1)`. Mean life : Mean life of a radioactive substance is the time at which the rate of disintegration (ie., activity) as well as the number of nuclides left undecayed have been reduced to `e^(-1)(or 1/eth)` of their initial values. SI unit of mean life is second.
Disintegration constant is reciprocal of mean life i.e, `lambda = 1/tau`, where `tau` is the mean life.