# NEET Chemistry The Solid State Questions Solved

BOARD

Explain how you can determine the atomic mass of an unknown metal if you know its mass density and the dimensions of unit cell of its crystal.

Suppose edge of the unit cell = a pm

Number of atoms present per unit cell = Z

$\therefore$ Volume of unit cell = (a pm)3

= (a$×$10-10cm)3 = a3 $×$ 10-30 cm3

Density of unit cell =    ...(i)

Mass of unit cell = Number of atoms in the unit cell $×$ mass of each atom = Z $×$m

Mass of each atom =  = $\frac{M}{{N}_{0}}$

Substituting these values in equation (i), we get

Density of unit cell = $\frac{Z×M}{{a}^{-3}×{10}^{-30}×{N}_{0}}$

If a is in cm, d = $\frac{Z×M}{{a}^{3}×{N}_{0}}$ g/cm3

$\therefore$ Molar mass can be calculated as

M= $\frac{d×{a}^{3}×{N}_{0}}{Z}$

Difficulty Level:

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