Question

The half-lives of two parallel path reaction are 4 hrs and 12 hrs respectively. The average half-life for the decay of A is ______ hrs.

Answer 1

$k=k_B+k_C$

$\frac{0.693}{t_{1/2}}=\frac{0.693}{t_{1/2}B}+\frac{0.693}{t_{1/2}C}$

$\frac{0.693}{t_{1/2}}=\frac{0.693}{4}+\frac{0.693}{12}$

$\frac{1}{t_{1/2}}=\frac{1}{4}+\frac{1}{12}$

$\frac{1}{t_{1/2}}=\frac{12+4}{4\times 12}=\frac{1}{3}$

$t_{1/2}=3$

Thus, the average half-life for the decay of A is 3 hrs.