Until the early $1950$s$,$ a paint containing radium$-226$ was used to make the dials on some clocks, watches, and aircraft instruments glow in the dark. Radium$-226$ has a decay constant of $1\mathrm{.}98{10}^{-11}{s}^{-1}.$

$($a$)$ If the activity of one of these clocks is $0\mathrm{.}10$ MBq $,$ how many atoms of radium$-226$ are on the dial?

$($b$)$ Calculate the mass of radium on the dial.

$($c$)$ The half$-$life of radium is $1600$ years. Calculate the activity that the clock will have in $5000$ years.