Ais the time required for one half of the nuclei in a radio- isotope to decay.

A half-life is the time required for one half of the nuclei in a radio- active isotope to decay.

Explanation:

A radio-active isotope is an isotope which undergoes radioactive decay.

Radioactive decay is a spontaneous process in which the nucleus of an atom changes its state (turning into a different nucleus, or de-exciting), emitting radiation, which can be of three different types: alpha, beta or gamma.

The half-life of a radio-active isotope is the time required for half of the nuclei of the initial sample to decay.

The law of radio-active decay can be expressed as follows:

where

N(t) is the number of undecayed nuclei left at time t

N0 is the initial number of nuclei

t is the time

is the half-life

We see that when (that means, when 1 half-life has passed), the number of undecayed nuclei left is

So, half of the initial nuclei.