The diameter of drop of mercury is 1.0 mm. The volume of drop is equal to the volume of sphere, thus, volume of mercury drop will be:
![V=\frac{4}{3}\pi r^{3}](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B4%7D%7B3%7D%5Cpi%20r%5E%7B3%7D)
Here, r is radius of drop.
Radius of drop can be calculated as:
![r=\frac{d}{2}=\frac{1 mm}{2}=0.5 mm](https://tex.z-dn.net/?f=r%3D%5Cfrac%7Bd%7D%7B2%7D%3D%5Cfrac%7B1%20mm%7D%7B2%7D%3D0.5%20mm)
Convert the unit into cm
1 mm=0.1 cm
thus,
0.5 mm=0.05 cm
Volume of sphere will be:
![V=\frac{4}{3}(3.14) (0.05 cm)^{3}=5.23\times 10^{-4}cm^{3}](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B4%7D%7B3%7D%283.14%29%20%280.05%20cm%29%5E%7B3%7D%3D5.23%5Ctimes%2010%5E%7B-4%7Dcm%5E%7B3%7D)
Now, density of mercury is ![13.6 g/cm^{3}](https://tex.z-dn.net/?f=13.6%20g%2Fcm%5E%7B3%7D)
Mass can be calculated as follows:
![m=d\times V=13.6 g/cm^{3}\times 5.23\times 10^{-4}cm^{3}=7.12\times 10^{-3}g](https://tex.z-dn.net/?f=m%3Dd%5Ctimes%20V%3D13.6%20g%2Fcm%5E%7B3%7D%5Ctimes%205.23%5Ctimes%2010%5E%7B-4%7Dcm%5E%7B3%7D%3D7.12%5Ctimes%2010%5E%7B-3%7Dg)
Molar mass of mercury is 200.59 g/mol thus, number of moles will be:
![n=\frac{m}{M}=\frac{7.12\times 10^{-3}g}{200.59 g/mol}=3.55\times 10^{-5} mol](https://tex.z-dn.net/?f=n%3D%5Cfrac%7Bm%7D%7BM%7D%3D%5Cfrac%7B7.12%5Ctimes%2010%5E%7B-3%7Dg%7D%7B200.59%20g%2Fmol%7D%3D3.55%5Ctimes%2010%5E%7B-5%7D%20mol)
In 1 mole of a substance there are
atoms thus,
will have:
![N=3.55\times 10^{-5}mol\times 6.023\times 10^{23}atoms/mol=2.14\times 10^{19} atoms](https://tex.z-dn.net/?f=N%3D3.55%5Ctimes%2010%5E%7B-5%7Dmol%5Ctimes%206.023%5Ctimes%2010%5E%7B23%7Datoms%2Fmol%3D2.14%5Ctimes%2010%5E%7B19%7D%20atoms)
Therefore, number of atoms in a drop of mercury will be
.