The activity of a radioactive sample falls from 700 s ^ - 1 to 500...

From equation of radioactivity. ${A}_{t} = {A}_{0}{e}^{- \lambdat}$

$\ln \left[\dfrac{{A}_{0}}{{A}_{t}}\right] = \lambdat$

$⇒ \ln \left[\dfrac{700}{500}\right] = \lambda ( 30min )$ ------\left(1\right)$</p><p>also</p><p>$⇒ \ln 2 = \lambda{t}_{1/2}$--------\left(2\right)$

$( ii ) / ( i )$

$⇒ \dfrac{\ln 2}{\ln ( 7 / 5 )} = \dfrac{{t}_{1/2}}{( 30min )} ⇒ ( 2 . 06004 ) 30 = {t}_{1/2} = 61 . 8min$

$\approx 62min$