The no. of atoms in face centred cubic and hexagonal unit cells respectively are
(a)6,4
(b)4,6
(c)1,6
(d)2,6
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Answers
Answer:
The number of atoms per unit cell in a simple cubic, face-centered cubic and body-centred cubic are 1,4,2 respectively.
(1)
The number of atoms contained in one simple cubic unit cell of monoatomic substance is 1.
8 atoms are present at 8 corners of a simple cubic unit cell. Each atom contributes one eigth to the unit cell. Total contribution =8×
8
1
=1
(2)
The number of atoms contained in one face-centred cubic unit cell of monoatomic substance is 4.
8 atoms are present at 8 corners of a fcc unit cell. Each atom contributes one eigth to the unit cell. Total contribution =8×
8
1
=1
6 atoms are present at 6 corners of a fcc unit cell. Each atom contributes one half to the unit cell. Total contribution =6×
2
1
=3
Total number of atoms in one fcc unit cell =1+3=4.
(3)
The number of atoms contained in one body-centred cubic unit cell of monoatomic substance is 2.
8 atoms are present at 8 corners of a bcc unit cell. Each atom contributes one eigth to the unit cell. Total contribution =8×
8
1
=1
1 atom is present at body centre of a bcc unit cell. The atom contributes fully to the unit cell. Total contribution =1×
1
1
=1
Total number of atoms in one fcc unit cell =1+1=2.