Answer
$2.4\times10^{24}$ carbon atoms
Work Step by Step
Start by converting 200mg to g by dividing by 1000.
$200$ mg$\div1000=0.2$ g
The diamond is 24 carats, so multiply 0.2 by 24 to find how many grams total of carbon there are.
$0.2$ g$\times24=4.8$ g
The molar mass of carbon is 12.011 g/mol. Convert 4.8 g to moles.
$\frac{4.8 g}{1}\times\frac{1mol}{12.011g}\approx0.4mol$
One mole of something equals $6.022\times10^{23}$ individual things.
So, multiply the amount of moles by $6.022\times10^{23}$ to get the number of atoms:
$0.4mol\times(6.022\times10^{23})=2.4\times10^{24}$ atoms
