NEET 2022 — Chemistry solution

NEET2022Chemistry

Copper crystallises in fcc unit cell with cell edge length of $3.608 \times 1 0^{- 8}$ cm. The density of copper is 8.92 g cm $^{- 3}$ . Calculate the atomic mass of copper.

A
31.55 u
B
60 u
C
65 u
D
63.1 u

Solution

Density of a crystal: $d = \frac{Z \cdot M}{N _{A} \cdot a ^{3}}$ , where $Z$ is the number of atoms per unit cell ( $Z = 4$ for fcc), $M$ is the molar mass, $N_{A}$ is Avogadro's number, and $a$ is the cell edge.

Solving for $M$ : $M = \frac{d \cdot N _{A} \cdot a ^{3}}{Z}$ .

$a^{3} = (3.608 \times 1 0^{- 8})^{3} \approx 4.70 \times 1 0^{- 23}$ cm $^{3}$ .

$M = \frac{8.92 \times 6.022 \times 1 0 ^{23} \times 4.70 \times 1 0 ^{- 23}}{4} \approx 63.1$ g/mol.

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