Question

If half-life period of a first order reaction is $x$ and $3/4th$ life period of the same reaction is $y$, how are $x$ and $y$ related to each other?

Answer 1

$t_{1/2}=\frac{\ln 2}{K}=x\left(given\right)$----------(1)
and $t=\ln \left(\frac{1}{(1-3/4)}\right)/k=y$.........(given)
or , $t=\frac{\ln \left(4\right)}{k}=y$----------(2)

So by (1) and (2)
$\frac{x}{y}=\frac{1}{2}$
or , $2x=y$