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 5 half-lives?

Answer 1

Answer:

6.56 g

Step-by-step explanation:

We can write the mass of radioactive isotope left after a time t by using the equation

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

where

$N_0 = 210 g$ is the initial amount of radioactive isotope

$t_{1/2}$ is the half-life

$t$ is the time

In this problem, we want to know the amount of radioactive isotope left after 5 half-lives, so after

$t=5 t_{1/2}$

Substituting into the equation, we have

$N(t)=(210 g) (\frac{1}{2})^{\frac{5 t_{1/2}}{t_{1/2}}}=\frac{210 g}{2^5}=6.56 g$