Hello! my question is -

What is the law of radioactive decay ?

and

derive the relationship betwen half life period and the disintegration constant.

the law of radioactive decay states that the rate of decay of nuclei present in a atom is directly propotional to the concentration of nuclie present (in other words directly propotional  to the no of nuclei)

Law of radioactive decay

Where,

N = Number of nuclei in the sample

ΔN = Amount undergoing decay

Δt = Time

Half life

The half life of a radioactive substance is defined as the average time for which the nuclei of the atoms of the radioactive substance exist.

Average life or mean life (τ)