Metal M crystallizes into a fcc lattice with the edge length of 4.0 x 10^-8 cm. The atomic mass of the metal is ____________ g / mol. (Nearest integer) (. Use : N_ A=6.02 x 10^23 mol^-1, density of metal, M=9.03 g cm^-3 )

rho=fracZ MN_A a^3 => M=frac9.03 x 6.02 x 10^23 x (4 x 10^-8)^34 =frac9.03 x 6.02 x 64 x 10^-14 \ =86.9 g mol^-1 \ = 87 g mol^-1

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Metal M crystallizes into a fcc lattice with the edge l... | (Chemistry) | DivineJEE

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Chemistry

Exam

Chemistry

Metal $\mathrm{M}$ 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)

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

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Explanation

$\rho=\frac{Z M}{N_{A} a^{3}} \Rightarrow M=\frac{9.03 \times 6.02 \times 10^{23} \times\left(4 \times 10^{-8}\right)^{3}}{4}$

$\begin{aligned} &=\frac{9.03 \times 6.02 \times 64 \times 10^{-1}}{4} \\ &=86.9 \mathrm{~g} \mathrm{~mol}^{-1} \\ &\approx 87 \mathrm{~g} \mathrm{~mol}^{-1} \end{aligned}$