Question

For a first order radio-active decay, the half-life period is :

• A. dependent on the square of the initial concentration
• B. dependent on first power of initial concentration
• C. dependent on the square root of initial concentration
• D. independent on initial concentration

Answer 1

The correct option is D independent on initial concentration

$t_{1/2}=\frac{1}{{\left(a\right)}^{n-1}}$
where, $n=$ order of reaction
$a=$ initial concentration
For first order reaction,
$n=1$
$t_{1/2}=\frac{1}{a^{1-1}}$
$a=\frac{1}{a^0}=0$
Thus, for a first order reaction, $t_{1/2}$ is independent on initial concentration.