Answer
34 hours.
Work Step by Step
Rate constant $k= \frac{0.693}{t_{1/2}}=\frac{0.693}{6.0\,h}$
$=0.1155\,h^{-1}$
We can obtain the time taken using integrated rate law which is
$\ln \frac{N_{t}}{N_{0}}=-kt$
$\ln \frac{1.0\times10^{-3}\,\mu g}{0.050\,\mu g}=-0.1155\,h^{-1}\times t$
$\implies -3.912023=-0.1155\,h^{-1}\times t$
$\implies t=\frac{-3.912023}{-0.1155\,h^{-1}}$
$=34\,h$
