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A metal crystallizes with a face-centered cubic lattice. The edge of the unit cell is 408 pm. The diameter of the metal atom is
- a)144 pm
- b)204 pm
- c)288 pm
- d)408 pm
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
A metal crystallizes with a face-centered cubic lattice. The edge of t...
Given:
- Metal crystallizes with a face-centered cubic lattice
- Edge of the unit cell = 408 pm
To find: Diameter of the metal atom
Formula:
In a face-centered cubic (fcc) lattice, the atoms are arranged in a pattern of a cube with an atom at each corner and an atom in the center of each face. The edge length of the unit cell (a) is related to the radius of the atom (r) by the formula:
a = 2√2r
We can rearrange the formula to find the radius (r) in terms of the edge length (a):
r = a/2√2
We are given the edge length (a) of the unit cell, so we can use the formula above to calculate the radius (r) of the atom. Then, we can double the radius to get the diameter of the atom.
Solution:
Substituting the given values in the formula:
a = 408 pm
r = a/2√2 = (408 pm)/(2√2) = 144 pm
The radius of the atom is 144 pm. To get the diameter, we double the radius:
Diameter = 2 × radius = 2 × 144 pm = 288 pm
Therefore, the diameter of the metal atom is option (c) 288 pm.
- Metal crystallizes with a face-centered cubic lattice
- Edge of the unit cell = 408 pm
To find: Diameter of the metal atom
Formula:
In a face-centered cubic (fcc) lattice, the atoms are arranged in a pattern of a cube with an atom at each corner and an atom in the center of each face. The edge length of the unit cell (a) is related to the radius of the atom (r) by the formula:
a = 2√2r
We can rearrange the formula to find the radius (r) in terms of the edge length (a):
r = a/2√2
We are given the edge length (a) of the unit cell, so we can use the formula above to calculate the radius (r) of the atom. Then, we can double the radius to get the diameter of the atom.
Solution:
Substituting the given values in the formula:
a = 408 pm
r = a/2√2 = (408 pm)/(2√2) = 144 pm
The radius of the atom is 144 pm. To get the diameter, we double the radius:
Diameter = 2 × radius = 2 × 144 pm = 288 pm
Therefore, the diameter of the metal atom is option (c) 288 pm.
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Community Answer
A metal crystallizes with a face-centered cubic lattice. The edge of t...
Use formula for BCC
RADIUS = √3a /4
= 1.41*143.82
= 287.64 € 288pm
RADIUS = √3a /4
= 1.41*143.82
= 287.64 € 288pm
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A metal crystallizes with a face-centered cubic lattice. The edge of the unit cell is 408 pm. The diameter of the metal atom isa)144 pmb)204 pmc)288 pmd)408 pmCorrect answer is option 'C'. Can you explain this answer?
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