Question

The carat is the unit of mass used by jewellers. One carat is exactly $200$mg. If the carbon atoms present in a $24$ carat diamond are $=2.408\times {10}^x$, then the value of $x$ is :

Answer 1

One carat $=200$ mg diamond.
$24$ carat $=200\times 24\times {10}^{-3}g$.

$=\frac{200\times 24\times {10}^{-3}}{12}g$ mole atom

$=0.4g$ mole atom.

$=0.4\times 6.02\times {10}^{23}$ atom.

$=2.408\times {10}^{23}$ atoms.

So, $x$ is $23$.