Question

The relation between half life ($T$) and decay constant ($\lambda$) is

Answer 1

The correct option is C $\lambda T=lo{g}_{e}2$
As per radiaoactive decay law, the radioactive decays per unit time are directly proportional to the total number of nuclei of radioactive compounds in the sample.
f the number of nuclei in a sample is N and the number of radioactive decays per unit time dt is dN then,
$$\frac{dN}{dt}=-\lambda N$$
Integrating both limits
$${\int }_{N_0}^N\frac{dN}{N}=–\lambda \underset{t_0}{\overset{t}{\int }}dt$$
Taking initial time $t_0$=0 we have