Answer:
length =2.5 x 10⁻⁸ m
# atoms = 2500
Explanation:
The volume of oil spread is the area of the spread time its thckness
V = A x Thickness . This thickness is approximately the same as the the length of the molecule once we have a monolayer.
Performing our calculation and converting the mL to m³:
0.10 mL x 1 x 10⁻⁶ m³/mL = 1 x 10⁻⁷ m³
Thickness = V/A = 1 x 10⁻⁶ m³ / 40 m² = 2.5 x 10⁻⁸ m
For the second part assuming the specific gravity of the nanosphere is the same as its bulk density, we can establish an equation relating the specific gravity of a nanosphere to the value given of 19.3 .
sp gravity = ρ gold/ ρ H₂O ⇒ ρ gold = 19.3 x 1 g/cm³
So by definition of specific gravity, we have that
Number of atoms of gold x mass (amu) / vol nanosphere = 19.3
diameter = 2.0 nm x 1 m/10⁹ nm x 100 cm/m = 2.0 x 10⁻⁷ m
r= /2 d = 1.0 x 10⁻⁷ m
Vnanosphere = 4/3 π r³ = 4/3 π (1 x 10⁻⁷ m)³ = 4.2 x 10⁻²¹ m³
mass of gold atoms = number of gold stoms x mass ( amu)
= # atoms x 197 x 1.66 x 10⁻²⁴ g/amu = # atoms x 3.3 x 10⁻²² g
sp gravity = ρ gold/ ρ H₂O ⇒ ρ gold = 19.3 x 1 g/cm³
d = 19.3 = (# atoms x 3.3 x 10⁻²² g) / 4.2 x 10⁻²¹ cm³ / 1g/cm³
⇒ # atoms = 2500
