Question

The half-life of a radioisotope is the amount of time it takes for

Answer 1

please note that, the decay law of a radioactive sample containing N atoms, is:
\[N(t)=N _{0}e ^{-t/\tau} \]
where tau is the half-life, and N_0 is the number of radio-isotopes at initial time, namely t=0.
So when t= tau, from the above equation, we have:
\[N(\tau)=N _{0}e ^{-1}=\frac{ N _{0} }{ e }\]
in other words, the half-life is the necessary time for which the numbers of radio-isotopes reduce itself by a factor 1/e

Answer 2

@QuishaBumpass

Answer 3

The half-life of a radioisotope is the amount of time it takes for half the sample to decay.

Answer 4

@Rrth1268 you are right! Sorry @QuishaBumpass

Answer 5

as @Rrth1268 said by definition half-life is the amount of time for half the sample to decay. If I call T the half-life, we can write:
\[N _{0}e ^{-T/\tau}=\frac{ N _{0} }{ 2 }\]
from which:
\[T= \tau *\log 2=\tau* 0.693\]