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JEE Main 202228 JulyEvening Shift
Exam
JEE Main
Year
2022
Date
28 July
Shift
Evening Shift
Subject
Chemistry
Chapter
Solid State

JEE Main 2022 · 28 July · Evening Shift · Chemistry · Solid State

Metal M crystallizes into a FCC lattice with the edge length of 4 ....

Metal MM crystallizes into a FCCFCC lattice with the edge length of 4.0×10−8cm4 . 0 \times {10}^{- 8}cm. The atomic mass of the metal is g/molg / mol.

(Use : NA=6.02×1023mol−1{N}_{A} = 6 . 02 \times {10}^{23}{mol}^{- 1}, density of metal, M=9.03gcm−3M = 9 . 03g{cm}^{- 3})

Correct answer

0

Step-by-step solution

Given ,a=4×10−8cma = 4 \times {10}^{- 8}cm

d=9.03g/mld = 9 . 03g / ml

d=ZMNAa3d = \dfrac{ZM}{{N}_{A}{a}^{3}}

Volume of a unit cell = a3, where a is the edge length

d is the density of the solid substance and M is the molar mass.

Mass of the unit cell = number of atoms in unit cell × mass of each atom =Z×mZ \times m

(Here z is the number of atoms present in one unit cell and m is the mass of a single atom)M=9.03×6.02×1023×64×10−244=86.97g/molM = \dfrac{9 . 03 \times 6 . 02 \times {10}^{23} \times 64 \times {10}^{- 24}}{4} = 86 . 97g / mol

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