Verified Solution • 2025–26 Session moderate

QJEEM22Ch6f6f: JEE Main 2022 Chemistry - Class 12 JEEM22Ch6f6f Solution: Metal crystallizes into a fcc lattice with the edge length of . …

Metal M\mathrm{M} crystallizes into a fcc lattice with the edge length of 4.0×10−8 cm4.0 \times 10^{-8} \mathrm{~cm} . The atomic mass of the metal is ____________ g/mol\mathrm{g} / \mathrm{mol} . (Nearest integer)

(\left(\right. Use : NA=6.02×1023 mol−1\mathrm{N}_{\mathrm{A}}=6.02 \times 10^{23} \mathrm{~mol}^{-1} , density of metal, M=9.03 g cm−3\mathrm{M}=9.03 \mathrm{~g} \mathrm{~cm}^{-3} )

Step-by-Step Verified Solution

ρ=ZMNAa3⇒M=9.03×6.02×1023×(4×10−8)34\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}

amp;=9.03×6.02×64×10−14amp;=86.9 g mol−1amp;≈87 g mol−1\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}

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