Answer:
A) 0.203 g
Explanation:
A radioactive isotope is an isotope that decays over time. The equation that describes the radioactive decay or an isotope is
[tex]m(t)=m_0 (\frac{1}{2})^{\frac{t}{\tau}}[/tex]
where
[tex]m_0[/tex] is the initial mass of the isotope at time t = 0
[tex]m(t)[/tex] is the mass of the isotope after time t
t is the time
[tex]\tau[/tex] is the half-life of the isotope, which is the time taken for the amount of isotope to halve
In this problem, we have:
[tex]m_0 = 26 g[/tex] is the initial mass of the sample of Thorium-232
[tex]\tau=14 \cdot 10^9 y[/tex] is the half-life of the sample
Here we want to find the amount of thorium left after 7 half-lives, so when
[tex]t=7\tau[/tex]
Substituting into the equation, we find:
[tex]m(t)=m_0 (\frac{1}{2})^\frac{7\tau}{\tau}=(26)(\frac{1}{2})^7=0.203 g[/tex]
