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Question

# The number of atoms per unit cell in a simple cubic, face-centered cubic and body-centred cubic are ...... respectively.

A
1,4,2
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B
4,1,2
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C
2,4,1
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D
4,8,2
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Solution

## The correct option is A 1,4,2The 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 =8×18=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 =8×18=16 atoms are present at 6 corners of a fcc unit cell. Each atom contributes one half to the unit cell. Total contribution =6×12=3Total 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 =8×18=11 atom is present at body centre of a bcc unit cell. The atom contributes fully to the unit cell. Total contribution =1×11=1Total number of atoms in one fcc unit cell =1+1=2.

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