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  • Metal M crystallizes into a fcc lattice with the edge length of <img alt="4.0 \times 10^{-8} \mathrm{~cm}" src="https://entrancecorner.oncodecogs.com/gif.latex?4.0%20%5Ctimes%2010%5E%7B-8%7D%20%5Cm

Metal M crystallizes into a fcc lattice with the edge length of 4.0 \times 10^{-8} \mathrm{~cm}. The atomic mass of the metal is_________ \mathrm{g} / \mathrm{mol}. (Nearest integer)

(Use \mathrm{N}_{\mathrm{A}}=6.02 \times 10^{23} \mathrm{~mol}^{-1}, density of metal, \mathrm{M}=9.03 \mathrm{~g} \mathrm{~cm}^{-3} )

Option: 1

87


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

\mathrm{a= edge\, \, length= 4\times 10^{-8}cm}
\mathrm{d= 9.03\, g|ml}
\mathrm{d= \frac{Z\times M}{a^{3}\times N_{A}}}

\mathrm{\Rightarrow M= \frac{d\times N_{A}\times a^{3}}{Z}= \frac{9.03\times 6.02\times 10^{23}\times 64\times 10^{-24}}{4}}
                                               \mathrm{\simeq 87}

\mathrm{where\: Z= 4\left [ fcc \: lattice\right ]}
\mathrm{a^{3}= 64\times 10^{-24}}

Hence answer is 87

Posted by

Gaurav

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