(B) The formula for density is $d = \frac{n \times M}{a^3 \times N_A}$.Given:$d = 7.2 \, g \, cm^{-3}$$a = 289 \, pm = 289 \times 10^{-10} \, cm$$M =

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(B) The formula for density is $d = \frac{n \times M}{a^3 \times N_A}$.Given:$d = 7.2 \, g \, cm^{-3}$$a = 289 \, pm = 289 \times 10^{-10} \, cm$$M = 52 \, g \, mol^{-1}$$N_A = 6.02 \times 10^{23} \, mol^{-1}$Rearranging for $n$:$n = \frac{d \times a^3 \times N_A}{M}$$n = \frac{7.2 \times (289 \times 10^{-10})^3 \times 6.02 \times 10^{23}}{52}$$n = \frac{7.2 \times 2.41 \times 10^{-23} \times 6.02 \times 10^{23}}{52}$$n = \frac{7.2 \times 2.41 \times 6.02}{52} \approx 2$Since the number of atoms per unit cell $n = 2$, the unit cell is $BCC$ (Body-Centered Cubic).

Class 12 Chemistry Solid State Mathematical analysis of cubic system and Bragg’s equation

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The density of chromium metal is $7.2 \, g \, cm^{-3}$. If the edge length of the unit cell is $289 \, pm$, determine the type of unit cell (Simple Cubic, Body-Centered Cubic, or Face-Centered Cubic). [Atomic mass of $Cr = 52 \, a.m.u.$, $N_A = 6.02 \times 10^{23} \, mol^{-1}$]

A
$SCC$
B
$BCC$
C
$FCC$
D
$HCP$

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Class 12

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Solid State

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Mathematical analysis of cubic system and Bragg’s equation

An element crystallises in a $bcc$ type of unit cell. The density and edge length of the unit cell are $4 \ g \ cm^{-3}$ and $500 \ pm$ respectively. What is the atomic mass of the element?

EasyMHT CET 2020

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Calculate the number of unit cells present in $1 \text{ g}$ of a metal if the product of the density of the metal and the volume of the unit cell is $2.5 \times 10^{-22} \text{ g}$.

DifficultMHT CET 2026

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An atomic substance $A$ of molar mass $12 \ g \ mol^{-1}$ has a cubic crystal structure with an edge length of $300 \ pm$. The number of atoms present in one unit cell of $A$ is $.....$ (Nearest integer). Given the density of $A$ is $3.0 \ g \ cm^{-3}$ and $N_{A} = 6.02 \times 10^{23} \ mol^{-1}$.

MediumJEE MAIN 2023

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The radius of $K^{+}$ is $133 \ pm$ and that of $Cl^{-}$ is $181 \ pm$. The volume of the unit cell of $KCl$ expressed in $10^{-22} \ cm^{3}$ is

MediumKVPY 2014

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Calculate the number of atoms in $100 \, g$ of a crystal that crystallizes in an $fcc$ structure, given that its density is $10 \, g/cm^3$ and the edge length is $200 \, pm$.

Medium

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The density of chromium metal is $7.2 \, g \, cm^{-3}$. If the edge length of the unit cell is $289 \, pm$, determine the type of unit cell (Simple Cubic, Body-Centered Cubic, or Face-Centered Cubic). [Atomic mass of $Cr = 52 \, a.m.u.$, $N_A = 6.02 \times 10^{23} \, mol^{-1}$]

Similar Questions

An element crystallises in a $bcc$ type of unit cell. The density and edge length of the unit cell are $4 \ g \ cm^{-3}$ and $500 \ pm$ respectively. What is the atomic mass of the element?

Calculate the number of unit cells present in $1 \text{ g}$ of a metal if the product of the density of the metal and the volume of the unit cell is $2.5 \times 10^{-22} \text{ g}$.

An atomic substance $A$ of molar mass $12 \ g \ mol^{-1}$ has a cubic crystal structure with an edge length of $300 \ pm$. The number of atoms present in one unit cell of $A$ is $.....$ (Nearest integer). Given the density of $A$ is $3.0 \ g \ cm^{-3}$ and $N_{A} = 6.02 \times 10^{23} \ mol^{-1}$.

The radius of $K^{+}$ is $133 \ pm$ and that of $Cl^{-}$ is $181 \ pm$. The volume of the unit cell of $KCl$ expressed in $10^{-22} \ cm^{3}$ is

Calculate the number of atoms in $100 \, g$ of a crystal that crystallizes in an $fcc$ structure, given that its density is $10 \, g/cm^3$ and the edge length is $200 \, pm$.

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