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The length of body diagonal of body centred cubic unit cell is 728 pm. If the radius of cation is 231 pm, the radius of the anion is
- a)497 pm
- b)133 pm
- c)288 pm
- d)398 pm
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
The length of body diagonal of body centred cubic unit cell is 728 pm...
∵ 2(r+ + r- ) = 728
r+ + r- = 364
r = 364 - 231
= 133 pm
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The length of body diagonal of body centred cubic unit cell is 728 pm...
To find the radius of the anion in a body-centered cubic (BCC) unit cell, we can use the relationship between the length of the body diagonal and the radius of the cation.
1. Relationship between the length of the body diagonal and the radius of the cation:
In a BCC unit cell, the body diagonal is equal to four times the radius of the cation (√3a). Here, 'a' represents the edge length of the unit cell.
So, √3a = 4r, where 'r' is the radius of the cation.
2. Determining the length of the body diagonal:
Given that the length of the body diagonal is 728 pm (picometers), we can substitute this value into the equation.
√3a = 4r
728 = 4r
r = 728/4
r = 182 pm
3. Determining the radius of the anion:
In a BCC unit cell, the cation is present at the corner of the unit cell, and the anion is located at the center of the unit cell. The anion is surrounded by eight cations.
The radius of the anion (R) can be determined using the relationship:
R = (2√3 - 4)r
Substituting the value of 'r' we found earlier:
R = (2√3 - 4)(182 pm)
R ≈ 133 pm
Therefore, the radius of the anion is approximately 133 pm. Hence, the correct answer is option 'B'.
1. Relationship between the length of the body diagonal and the radius of the cation:
In a BCC unit cell, the body diagonal is equal to four times the radius of the cation (√3a). Here, 'a' represents the edge length of the unit cell.
So, √3a = 4r, where 'r' is the radius of the cation.
2. Determining the length of the body diagonal:
Given that the length of the body diagonal is 728 pm (picometers), we can substitute this value into the equation.
√3a = 4r
728 = 4r
r = 728/4
r = 182 pm
3. Determining the radius of the anion:
In a BCC unit cell, the cation is present at the corner of the unit cell, and the anion is located at the center of the unit cell. The anion is surrounded by eight cations.
The radius of the anion (R) can be determined using the relationship:
R = (2√3 - 4)r
Substituting the value of 'r' we found earlier:
R = (2√3 - 4)(182 pm)
R ≈ 133 pm
Therefore, the radius of the anion is approximately 133 pm. Hence, the correct answer is option 'B'.
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The length of body diagonal of body centred cubic unit cell is 728 pm. If the radius of cation is 231 pm, the radius of the anion isa)497 pmb)133 pmc)288 pmd)398 pmCorrect answer is option 'B'. Can you explain this answer?
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