Answer
$1.00*10^{22}\text{ atoms C}$
Work Step by Step
$1.00 \text{ carat C} = 0.200 \text{ grams C}*\frac{1 \text{ mol C}}{12.011 \text{ grams C}}*\frac{6.0221*10^{23} \text{atoms C}}{1 \text{ mol C}}=1.00*10^{22}\text{ atoms C}$
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