CBSE Class 12-science Answered

According to radioactive decay law the rate of disintegration of a radioactive substance at an instant is directly proportional to the number of nuclei in the Radioactive substance at that time i.e.

N = N_o e^-λt, Where symbols have their usual meanings Consider a radioactive substance having No atoms initially at time (t = o). After time (t) no. of atoms left undecayed be N. If dN is the no. of atoms decayed in time dt then according to radioactive decay law:

Where is decay constant and negative sing indicates that a radioactive sample Goes on decreasing whit time

Equation (1) can also be written as

integrating - both - the sides

log N = λt + K  .............................(ii)

Where K is constant of integration

When t = o, N = No

K = loge No

Substituting K in equation (ii)

log N = log N =- λt

or, log

N = N e^-λt