Question

calculate the number of atom in fee unit cell​

Answer 1

Answer:

$\underline{\huge{Answer:-}}$

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.

Answer 2

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.