$($a$)$ In a sample of $20,000$ atoms, if $400$ decay in $8$ seconds what is the

radioactivity, measured in mCi, of the sample?

$($b$)$ In order to produce a level of radioactivity of $1$ mCi, how many nuclei of

$99$mTc $($$=3\mathrm{.}22$x$10-5$ s$-1)$ must be present? What mass of the radiotracer does this

correspond to$?($Avogadro$$s number is $6\mathrm{.}02$x$1023).$

$($c$)$ A radioactive sample of $99$mTc contains $10$ mCi activity at $9$ am$.$ What is the

radioactivity of the sample at $12$ pm on the same day?