Question

For a first-order reaction with the rate constant '$k$' and initial concentration '$a$', the half-life period is given by:

• A. $\frac{ln2}{k}$
• B. $\frac{1}{k}$
• C. $\frac{3}{2k{a}^2}$
• D. none of the above

Answer 1

The correct option is A $\frac{ln2}{k}$

$\ln \left(\frac{N}{N_o}\right)=-kt$
So for $t_{\frac{1}{2}}$ we know $N_{\frac{1}{2}}={N_o}_{\frac{1}{2}},$
$\ln \left(\frac{N}{{2N}_o}\right)=-k{t}_{\frac{1}{2}}-\ln \left(\frac{1}{2}\right)=k{t}_{\frac{1}{2}}$
$t_{\frac{1}{2}}=\frac{\ln \left(2\right)}{k}⟶$Option(A)