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What is the ratio of the nearest neighbour distance to the next nearest neighbour distance in a simple cubic crystal?
- a)1:√3
- b)1:√2
- c)1:1/√2
- d)none of these
Correct answer is option 'B'. Can you explain this answer?
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What is the ratio of the nearest neighbour distance to the next neares...
We know, in a simple cubic lattice all atoms are at eight corners of cubic lattice of length a.
So, In a simple cubic lattice, the distance of nearest neighbour d1 = a and the distance of next nearest neighbour d1 = a√2
So, In a simple cubic lattice, the distance of nearest neighbour d1 = a and the distance of next nearest neighbour d1 = a√2
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What is the ratio of the nearest neighbour distance to the next neares...
The ratio of the nearest neighbour distance to the next nearest neighbour distance in a simple cubic crystal can be calculated as follows:
In a simple cubic lattice, each atom is surrounded by 6 nearest neighbours, located at a distance equal to the lattice constant (a). The next nearest neighbours are located diagonally across the face of the cube and there are 12 of them. The distance to the next nearest neighbours can be calculated using the Pythagorean theorem:
Next nearest neighbour distance (d) = √(a^2 + a^2) = a√2
Therefore, the ratio of the nearest neighbour distance to the next nearest neighbour distance is:
Nearest neighbour distance : Next nearest neighbour distance = a : a√2
Simplifying this ratio, we divide both terms by a:
Nearest neighbour distance : Next nearest neighbour distance = 1 : √2
Therefore, the ratio of the nearest neighbour distance to the next nearest neighbour distance in a simple cubic crystal is 1 : √2.
In a simple cubic lattice, each atom is surrounded by 6 nearest neighbours, located at a distance equal to the lattice constant (a). The next nearest neighbours are located diagonally across the face of the cube and there are 12 of them. The distance to the next nearest neighbours can be calculated using the Pythagorean theorem:
Next nearest neighbour distance (d) = √(a^2 + a^2) = a√2
Therefore, the ratio of the nearest neighbour distance to the next nearest neighbour distance is:
Nearest neighbour distance : Next nearest neighbour distance = a : a√2
Simplifying this ratio, we divide both terms by a:
Nearest neighbour distance : Next nearest neighbour distance = 1 : √2
Therefore, the ratio of the nearest neighbour distance to the next nearest neighbour distance in a simple cubic crystal is 1 : √2.
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What is the ratio of the nearest neighbour distance to the next nearest neighbour distance in a simple cubic crystal?a)1:√3b)1:√2c)1:1/√2d)none of theseCorrect answer is option 'B'. Can you explain this answer?
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