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The radius of an atom of an element is 55 pm. What is the edge length of the unit cell if it is body-centred cubic?
- a)144.6 pm
- b)163.4 pm
- c)127.0 pm
- d)123.5 pm
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
The radius of an atom of an element is 55 pm. What is the edge length ...
Explanation: Given,
Interionic radius (r) = 55 pm
Edge length (a) =?
For BCC, r =
x a
Or a =
x r= 4 x 55/1.732 = 127 pm.
Interionic radius (r) = 55 pm
Edge length (a) =?
For BCC, r =
x aOr a =
x r= 4 x 55/1.732 = 127 pm.Most Upvoted Answer
The radius of an atom of an element is 55 pm. What is the edge length ...
To solve this problem, we need to understand the concept of a body-centered cubic (BCC) unit cell and the relationship between the radius of an atom and the edge length of the unit cell.
Body-Centered Cubic (BCC) Unit Cell:
A BCC unit cell is a type of crystal lattice structure where atoms are located at the corners of the cube and one atom is present at the center of the cube. This arrangement results in a total of two atoms per unit cell.
Relationship between Atom Radius and Unit Cell Edge Length:
In a BCC unit cell, the body-centered atom is in contact with the eight corner atoms. The distance between the center of the body-centered atom and the corner atoms is equal to the edge length of the unit cell. Therefore, the edge length (a) of the BCC unit cell can be related to the radius (r) of the atom using the following equation:
a = 4r / sqrt(3)
Solution:
Given that the radius of the atom is 55 pm, we can substitute this value into the equation above to find the edge length (a) of the BCC unit cell.
a = 4 * 55 pm / sqrt(3)
a ≈ 127.0 pm
Therefore, the correct answer is option C, 127.0 pm.
Body-Centered Cubic (BCC) Unit Cell:
A BCC unit cell is a type of crystal lattice structure where atoms are located at the corners of the cube and one atom is present at the center of the cube. This arrangement results in a total of two atoms per unit cell.
Relationship between Atom Radius and Unit Cell Edge Length:
In a BCC unit cell, the body-centered atom is in contact with the eight corner atoms. The distance between the center of the body-centered atom and the corner atoms is equal to the edge length of the unit cell. Therefore, the edge length (a) of the BCC unit cell can be related to the radius (r) of the atom using the following equation:
a = 4r / sqrt(3)
Solution:
Given that the radius of the atom is 55 pm, we can substitute this value into the equation above to find the edge length (a) of the BCC unit cell.
a = 4 * 55 pm / sqrt(3)
a ≈ 127.0 pm
Therefore, the correct answer is option C, 127.0 pm.
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Community Answer
The radius of an atom of an element is 55 pm. What is the edge length ...
Explanation: Given,
Interionic radius (r) = 55 pm
Edge length (a) =?
For BCC, r = x a
Or a =x r= 4 x 55/1.732 = 127 pm.
Interionic radius (r) = 55 pm
Edge length (a) =?
For BCC, r =
x aOr a =
x r= 4 x 55/1.732 = 127 pm.
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