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Sodium has body centred packing. Distance between two nearest atoms is 3.7 Å . The lattice parameter is:
- a)4.3 Å
- b)3.0 Å
- c)8.6 Å
- d)6.8 Å
Correct answer is option 'A'. Can you explain this answer?
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Sodium has body centred packing. Distance between two nearest atoms is...
Explanation:
Body Centred Cubic (BCC) Structure:
- In a body centred cubic (BCC) structure, atoms are arranged in a cube with one atom at each corner and one atom at the centre of the cube.
- This arrangement results in a coordination number of 8 and a lattice parameter, which is the distance between two nearest atoms, of √3 times the atomic radius.
Given Information:
- Distance between two nearest atoms = 3.7 Å
Calculation:
- In a BCC structure, the distance between two nearest atoms (d) is related to the lattice parameter (a) by the formula:
d = a * √3 / 2
- Given that d = 3.7 Å, we can rearrange the formula to solve for the lattice parameter (a):
a = 2 * d / √3
Solving for the Lattice Parameter:
- Substituting d = 3.7 Å into the formula:
a = 2 * 3.7 / √3
a ≈ 4.3 Å
Therefore, the lattice parameter for a body centred cubic (BCC) structure with a distance between two nearest atoms of 3.7 Å is approximately 4.3 Å, which corresponds to option 'A'.
Body Centred Cubic (BCC) Structure:
- In a body centred cubic (BCC) structure, atoms are arranged in a cube with one atom at each corner and one atom at the centre of the cube.
- This arrangement results in a coordination number of 8 and a lattice parameter, which is the distance between two nearest atoms, of √3 times the atomic radius.
Given Information:
- Distance between two nearest atoms = 3.7 Å
Calculation:
- In a BCC structure, the distance between two nearest atoms (d) is related to the lattice parameter (a) by the formula:
d = a * √3 / 2
- Given that d = 3.7 Å, we can rearrange the formula to solve for the lattice parameter (a):
a = 2 * d / √3
Solving for the Lattice Parameter:
- Substituting d = 3.7 Å into the formula:
a = 2 * 3.7 / √3
a ≈ 4.3 Å
Therefore, the lattice parameter for a body centred cubic (BCC) structure with a distance between two nearest atoms of 3.7 Å is approximately 4.3 Å, which corresponds to option 'A'.
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Sodium has body centred packing. Distance between two nearest atoms is 3.7 . The lattice parameter is:a)4.3 b)3.0 c)8.6 d)6.8 Correct answer is option 'A'. Can you explain this answer?
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