JEE Advanced · 2017 · 21 May 2017 · Paper 1 · Solid State

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A crystalline solid of a pure substance has a face-centred cubic structure with a cell edge of 400 pm. If the density of the substance in the crystal is

8 g cm^{- 3}

, then the number of atoms present in 256 g of the crystal is

N \times 1 0^{24}

. The value of

N

Answer: 2

Solution

For an fcc structure,

Z = 4

atoms per unit cell.

Using the density formula:

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

8 = \frac{4 \times M}{6.022 \times 1 0 ^{23} \times ( 400 \times 1 0 ^{- 10} ) ^{3}}

M = 76.8 g mol^{- 1}

Number of atoms in 256 g:

\frac{256}{76.8} \times 6.022 \times 1 0^{23} = 2.0 \times 1 0^{24} atoms

Therefore,

N = 2

JEE Advanced · 2017 · 21 May 2017 · Paper 1 · Integer answer

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