A radioactive sample initially has mass 400 g and half-life 10 years. How much remains after 30 years?

Solution & explanation

1. Given: m₀ = 400 g; T½ = 10 years; t = 30 years.

2. Count elapsed half-lives.

   $$n=\frac{30}{10}=3$$

3. After the first half-life, halve 400 g.

   $$m_1=\frac{400}{2}=200$$

4. After the second, halve 200 g.

   $$m_2=\frac{200}{2}=100$$

5. After the third, halve 100 g.

   $$m_3=\frac{100}{2}=50$$

6. State the result with units: 50 g of the original radionuclide remains.

50 g