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AB crystallizes in a body centred cubic lattice with edge length 'a' equal to 387pm. The distance between two oppositely charged ions in the lattice is:
- a)335 pm
- b)250 pm
- c)200 pm
- d)300 pm
Correct answer is option 'A'. Can you explain this answer?
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AB crystallizes in a body centred cubic lattice with edge length a equ...
AB crystallizes in a body centred cubic lattice with edge length a equal to 387pm. The distance between two oppositely charged ions in the lattice is:
To determine the distance between two oppositely charged ions in the lattice, we need to understand the structure of a body-centred cubic (BCC) lattice and the arrangement of ions within it.
Body-Centred Cubic (BCC) Lattice:
In a BCC lattice, the lattice points are located at the corners and at the centre of the cube. This arrangement results in a total of two lattice points per unit cell.
Calculating the Distance:
To calculate the distance between two oppositely charged ions, we need to consider the arrangement of ions in the lattice.
Step 1: Determine the length of the body diagonal of the unit cell.
The body diagonal of a cube can be calculated using the formula: d = a√3, where "d" is the length of the body diagonal and "a" is the edge length of the cube.
Given that the edge length (a) is 387 pm, we can calculate the length of the body diagonal (d) as follows:
d = 387 pm * √3 = 669.02 pm
Step 2: Calculate the distance between two oppositely charged ions.
Since the body-centred lattice consists of two lattice points, one at the centre and the other at a corner, the distance between them is equal to half the length of the body diagonal.
Therefore, the distance between two oppositely charged ions is:
Distance = d/2 = 669.02 pm / 2 = 334.51 pm
Rounding off to the nearest whole number, the distance between two oppositely charged ions in the lattice is 335 pm.
Hence, the correct answer is option 'A' - 335 pm.
To determine the distance between two oppositely charged ions in the lattice, we need to understand the structure of a body-centred cubic (BCC) lattice and the arrangement of ions within it.
Body-Centred Cubic (BCC) Lattice:
In a BCC lattice, the lattice points are located at the corners and at the centre of the cube. This arrangement results in a total of two lattice points per unit cell.
Calculating the Distance:
To calculate the distance between two oppositely charged ions, we need to consider the arrangement of ions in the lattice.
Step 1: Determine the length of the body diagonal of the unit cell.
The body diagonal of a cube can be calculated using the formula: d = a√3, where "d" is the length of the body diagonal and "a" is the edge length of the cube.
Given that the edge length (a) is 387 pm, we can calculate the length of the body diagonal (d) as follows:
d = 387 pm * √3 = 669.02 pm
Step 2: Calculate the distance between two oppositely charged ions.
Since the body-centred lattice consists of two lattice points, one at the centre and the other at a corner, the distance between them is equal to half the length of the body diagonal.
Therefore, the distance between two oppositely charged ions is:
Distance = d/2 = 669.02 pm / 2 = 334.51 pm
Rounding off to the nearest whole number, the distance between two oppositely charged ions in the lattice is 335 pm.
Hence, the correct answer is option 'A' - 335 pm.
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AB crystallizes in a body centred cubic lattice with edge length a equ...
2R=(root(3)×a)÷2=(1.732×387×10^-12)÷2=335pm
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AB crystallizes in a body centred cubic lattice with edge length a equal to 387pm. The distance between two oppositely charged ions in the lattice is:a)335 pmb)250 pmc)200 pmd)300 pmCorrect answer is option 'A'. Can you explain this answer?
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