Cobalt-60 has a half-life, which means that every half-life, the mass of the substance is halved.
If you start with an initial mass of cobalt-60 (let's say \(m_0\)), after each half-life, the mass can be calculated as follows:
- After 1 half-life: \(m_0 / 2\)
- After 2 half-lives: \(m_0 / 4\)
- After 3 half-lives: \(m_0 / 8\)
Let's say the initial mass of cobalt-60 is \(m_0 = 20\) g (as an example). After three half-lives, you would calculate:
- First half-life: \(20 , \text{g} / 2 = 10 , \text{g}\)
- Second half-life: \(10 , \text{g} / 2 = 5 , \text{g}\)
- Third half-life: \(5 , \text{g} / 2 = 2.5 , \text{g}\)
So, after three half-lives, there would be 2.5 g of cobalt-60 remaining.
Answer: 2.50 g