Answer:
6.25 g
Explanation:
The half-life of a radioactive isotope is the time needed for the mass of the sample to halve.
Here, we a radioactive polonium sample, whose half-life is
[tex]\tau_{1/2} = 103 y[/tex]
The mass of sample left after a time t is given by the equation
[tex]m(t) = m_0 (\frac{1}{2})^{t/t_{1/2})[/tex]
where
[tex]m_0 = 100 g[/tex] is the initial mass
[tex]\tau_{1/2} = 103 y[/tex] is the half-life
If we substitute t = 412 y , we find the mass of sample left:
[tex]m(t) = (100 g) (\frac{1}{2})^{412 y/103 y}=(100 g)(\frac{1}{2})^{1/4}=6.25 g[/tex]
