Question

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

Answer 1

Answer:

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:

$N(t) = N_0 (\frac{1}{2})^{t/t_{1/2}}$

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

$N(t) = N_0 (\frac{1}{2})^{t_{1/2}/t_{1/2}}=N_0 (\frac{1}{2})^1=\frac{N_0}{2}$

So, half of the initial nuclei.