Answer:
Explanation:
To find the relative density (
�
ρ) for a face-centered cubic (FCC) crystal structure, we can use the formula:
�
=
�
×
�
�
�
×
�
�
ρ=
N
A
×V
C
n×M
Where:
�
n is the number of atoms per unit cell (for FCC,
�
=
4
n=4).
�
M is the molar mass of the element.
�
�
N
A
is Avogadro's number (
6.02
×
1
0
23
6.02×10
23
atoms/mol).
�
�
V
C
is the volume of the unit cell.
From the given information:
�
=
0.128
r=0.128 (which seems to represent the atomic radius in angstroms, not
0.128
×
100
=
12.8
0.128×100=12.8 as written).
�
=
63.5
M=63.5 g/mol (assuming this is the molar mass of the element).
�
�
=
6.02
×
1
0
23
N
A
=6.02×10
23
atoms/mol.
�
�
=
474
×
1
0
−
23
V
C
=474×10
−23
cm³ (assuming this is the volume of the unit cell).
Substituting these values into the formula, we get:
�
=
4
×
63.5
6.02
×
1
0
23
×
474
×
1
0
−
23
ρ=
6.02×10
23
×474×10
−23
4×63.5
�
=
254
2.85
×
1
0
0
ρ=
2.85×10
0
254
�
≈
89.12
ρ≈89.12
Therefore, the relative density (
�
ρ) for the face-centered cubic (FCC) crystal structure is approximately
89.12
89.12.
