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  • An element M crystallises in a body centred cubic unit cell with a cell edge of . The dens

An element M crystallises in a body centred cubic unit cell with a cell edge of 300 \mathrm{pm}. The density of the element is 6.0 \mathrm{~g} \mathrm{~cm}^{-3}. The number of atoms present in 180 \mathrm{~g} of the element is____________ \times 10^{23} . (Nearest integer)

Option: 1

22.22


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

Given in question -

M = nody centered cubic
\Rightarrow Z= 2.

a = edge length = 300 pm
denisty = 6 g/cm3 

from the formula of density-
\mathrm{d= \frac{Z\times A}{a^{3}} \; (\text{A= mass of 1 atom of A})}
\mathrm{6\, g/cm^{3}= \frac{2\times A}{\left ( 300\times 10^{-10} \right )^{3}}}
\mathrm{A= 81\times 10^{-24\; }g}

\mathrm{atomic \; mass=81\times 10^{-24}\times 6.022\times 10^{23} }
                             \mathrm{48.7\, g/mol }
\mathrm{\text{no.of moles in 180g}= \frac{180}{48.7}= 3.7\, moles.}
 \mathrm{\therefore atoms\: of\: A= 3.7\times 6.022\times 10^{23}= 22.22\times 10^{23}\, atoms}
        

 

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Rishi

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