The average life $T$ and the decay constant $\lambda $ of a radioactive nucleus are related as
$T\lambda = 1$
$T = \frac{{0.693}}{\lambda }$
$\frac{T}{\lambda } = 1$
$T = \frac{C}{\lambda }$
The decay constant of the end product of a radioactive series is
The energy spectrum of $\beta$-particles [number $N(E)$ as a function of $\beta$-energy $E$] emitted from a radioactive source is
Half life of a radioactive substance is $T$. The time taken for all the nuclei to disintegrate will be
A radioactive sample consists of two distinct species having equal number of atoms $N_0$ initially. The mean-life of one species is $\tau $ and of the other is $5\tau $. The decay products in both cases is stable. The total number of radioactive nuclei at $t = 5\tau $ is
The radioactivity of a sample is $R_1$ at time $T_1$ and $R_2$ at time $T_2.$ If the half life of the specimen is $T.$ Number of atoms that have disintegrated in time $(T_2 - T_1)$ is proportional to