Respuesta :
Answer: The number of atoms in spherical gold nano particle are [tex]26.918\times 10^4[/tex]
Explanation:
- To calculate the volume of sphere, we use the equation:
[tex]V=\frac{4}{3}\pi r^3[/tex]
where,
r = radius of the sphere = [tex]10nm=10^{-6}cm[/tex] (Conversion factor: [tex]1nm=10^{-7}cm[/tex] )
Putting values in above equation, we get:
[tex]V=\frac{4}{3}\times 3.14\times (10^{-6})^3\\\\V=4.19\times 10^{-18}cm^3[/tex]
- To calculate mass of of the substance, we use the equation:
[tex]\text{Density of substance}=\frac{\text{Mass of substance}}{\text{Volume of substance}}[/tex]
Volume of gold = [tex]4.19\times 10^{-18}cm^3[/tex]
Density of gold = [tex]19.3g/cm^3[/tex]
Putting values in above equation, we get:
[tex]19.3g/cm^3=\frac{\text{Mass of gold}}{4.19\times 10^{-18}}\\\\\text{Mass of gold}=8.0867\times 10^{-17}g[/tex]
- To calculate the number of moles, we use the equation:
[tex]\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}}[/tex]
Mass of gold = [tex]8.8067\times 10^{-17}g[/tex]
Molar mass of gold = 196.97 g/mol
Putting values in above equation, we get:
[tex]\text{Moles of gold}=\frac{8.8067\times 10^{-17}g}{196.97g/mol}=4.47\times 10^{-9}moles[/tex]
- According to mole concept:
1 mole of an element contains [tex]6.022\time 10^{23}[/tex] number of atom
So, [tex]4.47\times 10^{-19}[/tex] moles of gold will contain = [tex]4.47\times 10^{-19}\times 6.022\times 10^{23}=26.918\times 10^4[/tex] number of atoms.
Hence, the number of atoms in spherical gold nano particle are [tex]26.918\times 10^4[/tex]
