Question

A radioactive polonium sample has a half-life of 103 years. How much of a 100 g sample would remain after 412 years?

Answer 1

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

$\tau_{1/2} = 103 y$

The mass of sample left after a time t is given by the equation

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

where

$m_0 = 100 g$ is the initial mass

$\tau_{1/2} = 103 y$ is the half-life

If we substitute t = 412 y , we find the mass of sample left:

$m(t) = (100 g) (\frac{1}{2})^{412 y/103 y}=(100 g)(\frac{1}{2})^{1/4}=6.25 g$