The half-life of a radioactive substance is the time taken for half of the substance to decay. For cobalt-60 (Co-60), after each half-life, the remaining mass of the substance is halved.
Let's denote the initial mass of cobalt-60 as \( m_0 \).
After one half-life, the remaining mass \( m_1 \) is: \[ m_1 = \frac{m_0}{2} \]
After two half-lives, the remaining mass \( m_2 \) is: \[ m_2 = \frac{m_1}{2} = \frac{m_0}{2^2} = \frac{m_0}{4} \]
After three half-lives, the remaining mass \( m_3 \) is: \[ m_3 = \frac{m_2}{2} = \frac{m_0}{2^3} = \frac{m_0}{8} \]
Thus, after three half-life cycles, the remaining mass of cobalt-60 will be \( \frac{m_0}{8} \). This means that 1/8 of the original mass will remain after three half-lives.