Verified Solution • 2025–26 Session moderate

QJEEM22Chf785: JEE Main 2022 Chemistry - Class 12 JEEM22Chf785 Solution: An element M crystallises in a body centred cubic unit cell…

An element M crystallises in a body centred cubic unit cell with a cell edge of 300 pm300 \,\mathrm{pm} . The density of the element is 6.0 g cm−36.0 \mathrm{~g} \mathrm{~cm}^{-3} . The number of atoms present in 180 g180 \mathrm{~g} of the element is ____________ ×1023\times 10^{23} . (Nearest integer)

Step-by-Step Verified Solution

MM is body certred cubic, ∴Z=2\therefore Z=2

Let mass of 1 atom of MM is AA

Edge length =300 pm=300 \,\mathrm{pm}

Density =6 g/cm3=6 \mathrm{~g} / \mathrm{cm}^3

∴6 g/cm3=Z×A(300×10−10)3=2×A27×10−24\therefore 6 \mathrm{~g} / \mathrm{cm}^3=\frac{\mathrm{Z} \times \mathrm{A}}{\left(300 \times 10^{-10}\right)^3}=\frac{2 \times \mathrm{A}}{27 \times 10^{-24}}

A=81×10−24 g\mathrm{A}=81 \times 10^{-24} \mathrm{~g}

∴\therefore Atomic mass =48.6 g=48.6 \mathrm{~g}

∴\therefore Mole in 180 g=18048.6=3.7180 \mathrm{~g}=\frac{180}{48.6}=3.7 moles

Atoms of M=3.7×6×1023\mathrm{M}=3.7 \times 6 \times 10^{23} =22.22×1023=22.22 \times 10^{23} atoms

Related Learning Resources & Exam Preparation

JEE Main PYQ Question Bank
Browse year-wise authentic previous years' questions with solutions
Authentic CBT Mock Tests
Simulate official exam environment with live timer and percentile scoring