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The edge length of a fcc is 508 pm. If the radius of cation is 110 pm, the radius of anion is
For fcc,
2(r_{+} + r_{}) = a
2(110 + r_{}) = 508
r_{} = 508/2  110 = 144 pm
A metal X crystallises in a facecentred cubic arrangement with the edge length 862 pm. What is the shortest separation of any two nuclei of the atom ?
For fcc arrangement , distance of nearest neighbour (d) is
= 609.6 pm
The edge length of sodium chloride unit cell is 564 pm. If the size of Cl^{} ion is 181 pm. The size of Na^{+} ion will be
2(r_{+} + r_{}) = a
2(2_{Na+} + r_{Cl}) = 564
2_{Na+ }= 564/2  181 = 101 pm
If the distance between Na^{+} and Cl^{} ions in NaCl crystals is 265 pm, then edge length of the unit cell will be?
In NaCl crystal , Edge length = 2 x distance between Na^{+} and Cl^{−}
=2 x 265 = 530 pm
The radius of Na^{+} is 95pm and that of Cl^{} is 181 pm. The edge length of unit cell in NaCl would be (pm).
a = (r_{+} + r_{}) = 2(95 + 181) = 552 pm
Copper crystallises in fcc with a unit cell length of 361 pm. What is the radius of copper atom?157 pm
For fcc,
r = √2 / 4 x a = √2 / 4 x 361
=
= 127 pm
Total volume of atoms present in a fcc unit cell of a metal with radius r is
a = 2√2 r
Volume of the cell = a3 = (2√2 r)^{3} = 16√2r^{3}
No. of shperes in fcc = 8 x 1/8 + 6 x 1/2 = 4
Volume of the four spheres = 4 x 4/3πr^{3}
= 16πr^{3}
The relation between atomic radius and edge length 'a' of a body centred cubic unit cell:
Distance between nearest neighbours, d = AD/2
In right angled △ABC,AC^{2 }= AB^{2} + BC^{2}
AC^{2} = a^{2 }+ a^{2} or AC = √2a
Now in right angled △ADC,
AD^{2} = AC^{2} + DC^{2}
∴ d = √3a / 2
Radius , r = d/2 = √3/4 a
Edge length of unit cell of Chromium metal is 287 pm with the arrangement. The atomic radius is the order of:
In bcc lattice, r = √3/4
r =
= 124.27 pm
The fraction of total volume occupied by the atoms present in a simple cube is
For simple cube,
Radius(r) = a / 2 [a = edge length]
Volume of the atom =
Packing fraction =
Volume of the sphere (atoms) in an unit cell.
For simple cubic, Z = 1 atom
Packing fraction =
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