Question

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

Answer 1

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

Step-by-step 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:

`N(t) = N_0 ((1)/(2))^{t/t_(1/2)}`

where

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

N0 is the initial number of nuclei

t is the time

`t_(1/2)` is the half-life

We see that when
`t=t_(1/2)` (that means, when 1 half-life has passed), the number of undecayed nuclei left is

`N(t) = N_0 ((1)/(2))^{t_(1/2)/t_(1/2)}=N_0 ((1)/(2))^1=(N_0)/(2)`

So, half of the initial nuclei.