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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Chemistry
Chapter
Solid State

NTA Abhyas 2020 · Chemistry · Solid State

A crystalline solid of a pure substance has a face-centred cubic...

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−3c{m}^{- 3} , then the number of atoms present in 256 g of the crystal is N×1024N \times 1{0}^{24} . The value of N is

Correct answer

2

Step-by-step solution

d=Z×M0NAa3d = \dfrac{Z \times \dfrac{{M}_{0}}{{N}_{A}}}{{a}^{3}}

(d = density)

8=4×M06×1023(4×10−10)38 = \dfrac{4 \times \dfrac{{M}_{0}}{6 \times 1{0}^{23}}}{( 4 \times 1{0}^{- 10}{)}^{3}}

M0=18×6×1.6{M}_{0} = \dfrac{1}{8 \times 6 \times 1.6}

Number of moles in 256 g =2568×6×1.6=103= \dfrac{256}{8 \times 6 \times 1.6} = \dfrac{10}{3}

Number of atoms =103×6×1023=2×1024= \dfrac{10}{3} \times 6 \times 1{0}^{23} = 2 \times 1{0}^{24}
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