Question

The half-life of Actinium 227 decays in 20 years. Calculate the mass of the element left when a 2kg sample was left for 160 years.

Answer 1

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:

$m(t) = m_0 (\frac{1}{2})^{-\frac{t}{\tau_{1/2}}}$

where

$m_0$ is the initial amount of the sample

t is the time

$\tau_{\frac{1}{2}}$ is the half-life of the isotope

For the sample of Actinium 227 in this problem,

$m_0 = 2 kg$

$\tau_{1/2}=20 years$

t = 160 years

Substituting into the equation,

$m(160) = (2 kg) (\frac{1}{2})^{-\frac{160}{20}}=0.0078 kg$

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