Answer
$7\times10^{-16}\,s$
Work Step by Step
Amount of radionuclide at the beginning $A_{0}=100$
Amount of radionuclide remaining
$A= 100.00-99.90=0.10$
Rate constant $k=\frac{0.693}{t_{1/2}}=\frac{0.693}{0.07\times10^{-15}\,s}=9.9\times10^{15}\,s^{-1}$
$\ln(\frac{A_{0}}{A})=kt$
$\implies \ln(\frac{100}{0.10})=6.9=9.9\times10^{15}\,s^{-1} \times t$
Or $t= \frac{6.9}{9.9\times10^{15}\,s^{-1} }=7\times10^{-16}\,s$
