Question

An element crystallizes into a structure which may be described by a cubic type of unit cell 7. having one atom in each corner of the cube and two atoms on one of its face diagonals. If the volume of this unit cell is 24 x 10-24 cm3 and density of the element is 7.20 gm/cm3, calculate number of atoms present in 200 gm of the element

Answer 1

Answer:

Number of atoms contributed in one unit cell = one atom from the eight corners + one atom from the two face diagonals = 1+1 = 2 atoms

Mass of one unit cell = volume × its density

                               = 24 × 10^–24 cm³ × 7.2 gm/ cm³

                               = 172.8 × 10^–24 gm

∴ 172.8 ×10^–24 gm is the mass of one unit cell i.e., 2 atoms

∴ 200 gm is the mass = 2 × 200 / 172.8 × 10^–24 atoms = 2.3148 × 10²⁴ atoms

Final answer: 2.3148 × 10²⁴ atoms

[Note: Some text books show its value as 3.472 × 10²⁴ atoms, i do not know how they are calculating.]

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