Given:
- Atomic substance A with molar mass M=12g mol−1
- Cubic crystal structure with edge length a=300pm=300×10−12m
- Density ρ=3.0g mL−1
- Avogadro's number NA=6.02×1023mol−1
First, calculate the volume of the unit cell V=a3=(300×10−12m)3=27×10−30m3.
Next, calculate the mass of the unit cell using the given density. Density is mass over volume, so mass
m=ρ⋅V=3.0g mL−1⋅27×10−30m3⋅10−6m31mL=81×10−24g.
Then, calculate the number of moles in one unit cell. The molar mass is mass over number of moles, so
n=Mm=12g mol−181×10−24g=6.75×10−26mol.
Finally, calculate the number of atoms in one unit cell. The Avogadro constant is the number of atoms per mole,
so number of atoms =n⋅NA=6.75×10−26mol⋅6.02×1023mol−1=4.06.
Rounding to the nearest integer, we get 4 atoms. So, there are 4 atoms present in one unit cell of substance A.