The mass of Actinium 227 left is 0.0078 kg
Explanation:
The amount of mass left of a radioactive isotope after time t is given by the equation:
[tex]m(t) = m_0 (\frac{1}{2})^{-\frac{t}{\tau_{1/2}}}[/tex]
where
[tex]m_0[/tex] is the initial amount of the sample
t is the time
[tex]\tau_{\frac{1}{2}}[/tex] is the half-life of the isotope
For the sample of Actinium 227 in this problem,
[tex]m_0 = 2 kg[/tex]
[tex]\tau_{1/2}=20 years[/tex]
t = 160 years
Substituting into the equation,
[tex]m(160) = (2 kg) (\frac{1}{2})^{-\frac{160}{20}}=0.0078 kg[/tex]
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