Question

Americium-241 is a radioactive substance used in smoke detectors. The half life of americium is 432 years. If a smoke detector initially contains 1 gram of Americium 241, how much will remain in 432 years?

Answer 1

Answer:

0.5 g

Explanation:

The half-life of a radioactive isotope is the time it takes for a certain amount of that isotope to halve.

In this case, we have an isotope of Americium-241, which has a half-life of

$\tau = 432 y$

This means that after 1 half-life (432 years), there will be an amount of americium equal to half its initial amount.

In this problem, the initial amount of americium is

$m_0 = 1 g$

Therefore, after 432 years (1 half-life), the amount of americium left will be half:

$m(432y) = \frac{m_0}{2}=0.5 g$