Concept explainers
(a)
Interpretation:
The packing efficiency of the simple cubic cell (1atom/cell) is to be determined.
Concept Introduction:
Packing efficiency of the cubic cell is calculated by the following formula:
(a)
Answer to Problem 62QAP
The packing efficiency of the simple cubic cell (1atom/cell) is 52 %.
Explanation of Solution
Given:
The volume of one atom is
The percentage of the total of solid occupied by the spherical atoms in the cell is said to be packing efficiency.
The mathematical formula for the packing efficiency is:
In cubic cell, edge length is denoted as ‘s’ and the radius as ‘r’.
The relation between edge length and radius of the simple cubic cell is:
Put the above values in (1):
And the relation between r and s:
2r = s
There is only one atom present in the simple cubic cell.
Therefore,
Packing efficiency = 52 %.
(b)
Interpretation:
The packing efficiency of face-centered cubic cell (4 atoms/cell) is to be determined.
Concept Introduction:
Packing efficiency of the cubic cell is calculated by the following formula:
(b)
Answer to Problem 62QAP
The packing efficiency of the face-centered cubic cell (4atom/cell) is 74%.
Explanation of Solution
Given:
The volume of one atom is
The percentage of the total of solid occupied by the spherical atoms in the cell is said to be packing efficiency.
The mathematical formula for the packing efficiency is:
In cubic cell, edge length is denoted as ‘s’ and the radius as ‘r’.
The relation between edge length and radius of the face-centered cubic cell is:
Put the above values in (1):
And the relation between r and s:
There are four atoms present in the face-centered cubic cell.
Therefore,
Packing efficiency = 74 %
(c)
Interpretation:
The packing efficiency of a body-centered cubic cell (2 atoms/cell) is to be determined.
Concept Introduction:
Packing efficiency of the cubic cell is calculated by the following formula:
(c)
Answer to Problem 62QAP
The packing efficiency of a body-centered cubic cell (2 atom/cell) is 68 %.
Explanation of Solution
Given:
The volume of one atom is
The percentage of the total of solid occupied by the spherical atoms in the cell is said to be packing efficiency. The mathematical formula for the packing efficiency is:
In cubic cell, edge length is denoted as ‘s’ and the radius as ‘r’.
The relation between edge length and radius of the body-centered cubic cell is:
Put the above values in (1):
The relation between r and s:
There are two atoms present in the body-centered cubic cell.
Therefore,
Packing efficiency = 68 %
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OWLV2 FOR MASTERTON/HURLEY'S CHEMISTRY:
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