Question

A metal crystallises in simple cubic lattice with edge length of 400 pm. Molar mass of the metal is 60 g mol" The density of metal will be (NA - 6* 1023 atoms mol) O 1.32 g cm3 O 1.56 g cm 02.12 g cm 3 O 1.91 g cm 3​

Answer 1

The density of the metal will be 1.56 g/cm³

Therefore, option (2) is correct.

Explanation:

Given:

Edge length of simple cubic lattice = 400 pm

Molar mass of metal = 60 g/mol

To find out:

Density of the metal

Solution:

Given that

$a=400$ pm $=400\times 10^{-12}=4\times 10^{-8}$ cm

$M=60$ g/mol

We know that density of the unit cell is given by

$\boxed{\rho=\frac{Z\times M}{N_0\times a^3}}$

For a simple cubic lattice,

$Z=1$

Hence,

$\rho=\frac{1\times 60}{6\times 10^{23}\times (4\times 10^{-8})^3}$

$\implies \rho=\frac{10}{64\times 10^{-1}}$ g/cc

$\implies \rho=1.5625$ g/cm³

Hope this answer is helpful.

Know More:

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