Question

The half-life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to half its initial mass.? starting with 210 grams of a radioactive isotope, how much will be left after 4 half-lives? ROUND TO NEAREST GRAM

Answer 1

In you notes it may be given that half life (\(t_{1/2}\)) as,
\(\displaystyle t_{1/2}=\frac{\ln(2)}{\lambda}\)

(or refere this http://en.wikipedia.org/wiki/Exponential_decay)

then \(\lambda=\frac{\ln(2)}{t_{1/2}}\)

Now to the main equation

\(N(4t_{1/2})=N_0e^{\lambda\times 4t_{1/2}}\)

replace \(\lambda\) from the previous derivation.