What will be the remaining mass of cobalt-60 after undergoing three half-life cycles?

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.