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In fcc crystal lattice, edge length is 400 pm. Find the diameter of greatest sphere which can be fitted into the interstitial vo id without distortion of lattice:
- a)58.54 pm
- b)117.08 pm
- c)29.54 pm
- d)414 pm
Correct answer is option 'B'. Can you explain this answer?
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In fcc crystal lattice, edge length is 400 pm. Find the diamete...
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In fcc crystal lattice, edge length is 400 pm. Find the diamete...
Given:
- Edge length of the FCC crystal lattice = 400 pm
To find:
- Diameter of the greatest sphere that can be fitted into the interstitial void without distorting the lattice
Explanation:
The face-centered cubic (FCC) crystal lattice consists of closely packed spheres where each sphere is in contact with 12 nearest neighboring spheres. In this lattice, the voids between the spheres are called interstitial voids.
Step 1: Calculate the length of the body diagonal:
The body diagonal of the cube can be calculated using the edge length (a) as follows:
Body diagonal (d) = a√3
Substituting the given value, we have:
d = 400 pm x √3
d ≈ 692.82 pm
Step 2: Calculate the radius of the greatest sphere:
The radius of the greatest sphere that can be fitted into the interstitial void is half the length of the body diagonal. Therefore:
Radius (r) = d/2
r ≈ 692.82 pm/2
r ≈ 346.41 pm
Step 3: Calculate the diameter of the greatest sphere:
Diameter (D) = 2r
D ≈ 2 x 346.41 pm
D ≈ 692.82 pm
Conclusion:
The diameter of the greatest sphere that can be fitted into the interstitial void without distorting the lattice is approximately 692.82 pm. Therefore, the correct option is B) 117.08 pm.
- Edge length of the FCC crystal lattice = 400 pm
To find:
- Diameter of the greatest sphere that can be fitted into the interstitial void without distorting the lattice
Explanation:
The face-centered cubic (FCC) crystal lattice consists of closely packed spheres where each sphere is in contact with 12 nearest neighboring spheres. In this lattice, the voids between the spheres are called interstitial voids.
Step 1: Calculate the length of the body diagonal:
The body diagonal of the cube can be calculated using the edge length (a) as follows:
Body diagonal (d) = a√3
Substituting the given value, we have:
d = 400 pm x √3
d ≈ 692.82 pm
Step 2: Calculate the radius of the greatest sphere:
The radius of the greatest sphere that can be fitted into the interstitial void is half the length of the body diagonal. Therefore:
Radius (r) = d/2
r ≈ 692.82 pm/2
r ≈ 346.41 pm
Step 3: Calculate the diameter of the greatest sphere:
Diameter (D) = 2r
D ≈ 2 x 346.41 pm
D ≈ 692.82 pm
Conclusion:
The diameter of the greatest sphere that can be fitted into the interstitial void without distorting the lattice is approximately 692.82 pm. Therefore, the correct option is B) 117.08 pm.
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In fcc crystal lattice, edge length is 400 pm. Find the diameter of greatest sphere which can be fitted into the interstitial vo id without distortion of lattice:a)58.54 pmb)117.08 pmc)29.54 pmd)414 pm Correct answer is option 'B'. Can you explain this answer?
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