$($a$)$ Silicon has three naturally occurring isotopes: $92\mathrm{.}23\%$ of ${?}^{28}Si,$ with an atomic weight of $27\mathrm{.}9769a,4\mathrm{.}68\%$ of ${?}^{29}Si,$ with an atomic weight of $28\mathrm{.}9765a,$ and $3\mathrm{.}09\%$ of ${?}^{30}Si,$ with an atomic weight of $29\mathrm{.}9738a.$ On the basis of these data, confirm that the average atomic weight of $Si$ is $28\mathrm{.}0854a.[4$ points$]$

$($b$)$ How many grams are there in one amu of a material? $[3$ points$]$

$($c$)$ Mole is taken in units of gram$-$mole. On this basis, how many atoms are there in a pound$-$mole of a substance? $[3$ points$]$