Question

$8.33\times {10}^x$ carbon atoms are present in a diamond weighing $200$ mg and of $20$ carat purity. Then, the value of $x$ is _______. write the value in the form of x/3.

Answer 1

Purity$=\frac{20}{24}\times 100=\frac{250}{3}g$.
($24$ carat is assumed to be $100\%$)
Pure diamond in $200mg$ sample$=\frac{200}{1000}\times \frac{250}{3}\times \frac{1}{100}=\frac{1}{6}g$
Number of moles $=\frac{1}{6}\times \frac{1}{12}g$ carbon.
Number of carbon atoms$=\frac{6.02\times {10}^{23}}{72}=8.33\times {10}^{21}$ atom.
So, value of $x$ is $21$.