Question

Consider the parallel first order reactions given above.
The half-life for the decay of $A$ is _________ hrs.

• A. $1$
• B. $3$
• C. $4$
• D. $12$

Answer 1

The correct option is B $3$

For parallel first order reaction,

$-\frac{dA}{dt}=(k_1+k_2)\left[A\right]=k\left[A\right]$

$t_{1/2}=\frac{In2}{k}=\frac{In2}{k_1+k_2}$

$=\frac{In2}{\frac{In2}{(t_{1/2}{)}_1}+\frac{In2}{(t_{1/2}{)}_2}}=\frac{(t_{1/2}{)}_1\times (t_{1/2}{)}_2}{(t_{1/2}{)}_1+(t_{1/2}{)}_2}$

$=\frac{4\times 12}{4+12}$ =3 hrs