A undergoes two parallel first-order reactions with k_1 = 4.0x10^-3 s^-1 and k_2 = 3.0x10^-3 s^-1. Using ln 2 = 0.693, find the half-life of A in seconds (nearest integer).

JEE Main levelNumerical answerDifficulty 2 of 3ck168

A undergoes two parallel first-order reactions with $k_{1} = 4.0 \times 1 0^{- 3} s^{- 1}$ and $k_{2} = 3.0 \times 1 0^{- 3} s^{- 1}$ . Using $ln 2 = 0.693$ , find the half-life of A in seconds (nearest integer).

Numerical answer type, answer in s, tolerance 1.

Parallel first-order paths give

k = k_{1} + k_{2} = 7.0 \times 1 0^{- 3} s^{- 1}

. Then

t_{1/2} = 0.693/ k = 0.693/ (7.0 \times 1 0^{- 3}) = 99.0 s

, i.e. about 99 s.