Chemistry

First-order decomposition means each substance decays independently at its own rate, determined by its half-life. The key insight is that after time $t$, the fraction remaining follows $N(t) = N_0 \cdot (1/2)^{t/t_{1/2}}$. Since $P$ and $Q$ have different half-lives, they'll decompose at different speeds over the same 54-minute period—count how many half-lives each completes to find what fraction survives.

First-order decomposition means each substance decays independently at its own rate, determined by its half-life. The key insight is that after time $t$, the fraction remaining follows $N(t) = N_0 \cdot (1/2)^{t/t_{1/2}}$. Since $P$ and $Q$ have different half-lives, they'll decompose at different speeds over the same 54-minute period—count how many half-lives each completes to find what fraction survives.