Verified Solution • 2025–26 Session moderate

QJEEM22Ch4276: JEE Main 2022 Chemistry - Class 12 JEEM22Ch4276 Solution: An element X has a body centred cubic (bcc) structure with a…

An element X has a body centred cubic (bcc) structure with a cell edge of 200 pm. The density of the element is 5 g cm −- 3. The number of atoms present in 300 g of the element X is _______________.

Given : Avogadro constant, NA = 6.0 ×\times 1023 mol −- 1.

Multiple Choice Options

  • A 5 NA
  • B 6 NA
  • C 15 NA
  • D 25 NA

Step-by-Step Verified Solution

ρ=Z×Ma3×NA\rho=\frac{Z \times M}{a^{3} \times N_{\mathrm{A}}}

Z=2 for bccZ=2 \text { for } b c c

amp;5 g/cm3=2×M(200×10−10 cm)3×6.0×1023⇒M=12 g\begin{aligned}& 5 \mathrm{~g} / \mathrm{cm}^{3}=\frac{2 \times M}{\left(200 \times 10^{-10} \mathrm{~cm}\right)^{3} \times 6.0 \times 10^{23}} \Rightarrow M=12 \mathrm{~g}\end{aligned}

12 g12 \mathrm{~g} of element contain =NA=N_{\mathrm{A}} atoms

300 g300 \mathrm{~g} of element contains =NA×30012=25NA=N_{\mathrm{A}} \times \frac{300}{12}=25 N_{\mathrm{A}}

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