Answer:
120 grams will be left after 180 years.
Step-by-step explanation:
A radioactive half-life refers to the amount of time it takes for half of the original isotope to decay and its given by
[tex]N(t)=N_0(\frac{1}{2})^\frac{t}{t_{1/2}}[/tex]
where,
[tex]N(t)[/tex] = quantity of the substance remaining
[tex]N_0[/tex] = initial quantity of the substance
[tex]t[/tex] = time elapsed
[tex]t_{1/2}[/tex] = half life of the substance
From the information given we know that:
And we want to find how much will be left. For this we use the above formula.
[tex]N(t)=480\left(\frac{1}{2}\right)^{\frac{180}{90}}\\\\N(t)=480\left(\frac{1}{2}\right)^2\\\\N(t)=480\cdot \frac{1}{2^2}=120[/tex]
120 grams will be left after 180 years.
