JEE Main · 2023 · 11 Apr 2023 · Shift 1 · Solid State

An atomic substance A of molar mass

12 g mol^{- 1}

has a cubic crystal structure with edge length of 300 pm . The no. of atoms present in one unit cell of A is ____. (Nearest integer)

Given the density of A is

3.0 g mL^{- 1}

and

N_{A} = 6.02 \times 1 0^{23} mol^{- 1}

Answer: 4

Solution

Using the formula for density of a crystal:

d = \frac{Z \times M}{N _{A} \times a ^{3}}

Rearranging:

Z = \frac{d \times N _{A} \times a ^{3}}{M}

Given: d = 3 g/cm³, M = 12 g/mol, a = 300 pm =

3 \times 1 0^{- 8}

cm,

N_{A} = 6.02 \times 1 0^{23}

mol⁻¹

Z = \frac{3 \times 6.02 \times 1 0 ^{23} \times ( 3 \times 1 0 ^{- 8} ) ^{3}}{12}

Z = \frac{3 \times 6.02 \times 1 0 ^{23} \times 27 \times 1 0 ^{- 24}}{12}

Z = \frac{3 \times 6.02 \times 27}{12 \times 10} = \frac{487.62}{120} = 4.06 \approx 4

JEE Main · 2023 · 11 Apr 2023 · Shift 1 · Integer answer

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