Gold has an atomic weight of 196.97 g/mol, and a density of 19.3 g/cm3. Approximately how many atoms are in a spherical gold nanoparticle 10 nm in diameter?

Question

asked Nov 23, 2020 196k views

1 Answer

Kartik Dolas · Answer 1 · 2020-11-27T20:02:19+0000

Answer: The number of atoms in spherical gold nano particle are

Step-by-step explanation:

$V=(4)/(3)\pi r^3$

where,

r = radius of the sphere =
10nm=10^(-6)cm (Conversion factor:
)

Putting values in above equation, we get:

$V=(4)/(3)* 3.14* (10^(-6))^3\\\\V=4.19* 10^(-18)cm^3$

$\text{Density of substance}=\frac{\text{Mass of substance}}{\text{Volume of substance}}$

Volume of gold =
4.19* 10^(-18)cm^3

Density of gold =
19.3g/cm^3

Putting values in above equation, we get:

$19.3g/cm^3=\frac{\text{Mass of gold}}{4.19* 10^(-18)}\\\\\text{Mass of gold}=8.0867* 10^(-17)g$

$\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}}$

Mass of gold =
8.8067* 10^(-17)g

Molar mass of gold = 196.97 g/mol

Putting values in above equation, we get:

$\text{Moles of gold}=(8.8067* 10^(-17)g)/(196.97g/mol)=4.47* 10^(-9)moles$

1 mole of an element contains
$6.022\time 10^(23)$ number of atom

So,
4.47* 10^(-19) moles of gold will contain =
4.47* 10^(-19)* 6.022* 10^(23)=26.918* 10^4 number of atoms.

Hence, the number of atoms in spherical gold nano particle are