(C) The formula for density $(d)$ is given by: $d = \frac{Z \times M}{N_A \times V}$ Rearranging for $Z$: $Z = \frac{d \times N_A \times V}{M}$ Volume

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

(C) The formula for density $(d)$ is given by: $d = \frac{Z \times M}{N_A \times V}$ Rearranging for $Z$: $Z = \frac{d \times N_A \times V}{M}$ Volume $(V)$ = $a \times b \times c = 4.2 \times 8.6 \times 8.3 \times 10^{-24} \, cm^3 = 299.712 \times 10^{-24} \, cm^3$ Substituting the values: $Z = \frac{3.3 \times 6.022 \times 10^{23} \times 299.712 \times 10^{-24}}{155}$ $Z = \frac{3.3 \times 6.022 \times 29.9712}{155} \approx \frac{595.6}{155} \approx 3.84$ Since $Z$ must be an integer,the number of formula units per unit cell is $4$.

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

Medium

In an orthorhombic crystal system,the values of $a$,$b$,and $c$ are $4.2 \, \mathring{A}$,$8.6 \, \mathring{A}$,and $8.3 \, \mathring{A}$ respectively. Given the molar mass of the solute is $155 \, g \, mol^{-1}$ and the density is $3.3 \, g \, cm^{-3}$,calculate the number of formula units $(Z)$ per unit cell.

A
$2$
B
$3$
C
$4$
D
$6$

Explore More

Browse All

Question Bank

All Subjects

Class 12 Questions

Class 12

Chemistry Questions

Chapter

Solid State

Subtopic

Mathematical analysis of cubic system and Bragg’s equation

Calculate the number of atoms in $5.4 \ g$ of a metal forming an $fcc$ structure,given that the unit cell volume $\left(a^3\right)$ multiplied by density $\left(\varrho\right)$ is $7.2 \times 10^{-22} \ g$.

MediumMHT CET 2025

View Solution

Copper crystallizes in an $fcc$ lattice with a unit cell edge length of $361 \ pm$. What is the radius of the copper atom in $pm$?

Medium

View Solution

If the edge length of a unit cell of $Li$ is $351 \, pm$, what is the radius of $Li$ (in $pm$)?

Easy

View Solution

Ferrous oxide has a cubic structure and each edge of the unit cell is $5.0 \, \mathring{A}$. Assuming the density of the oxide is $4.0 \, g \, cm^{-3}$,the number of $Fe^{2+}$ and $O^{2-}$ ions present in each unit cell will be ($M_w$ of $FeO = 72$)

Medium

View Solution

What is the number of atoms present per unit cell of aluminium having edge length $4 \ \mathring{A}$? (Given: density of $Al = 2.7 \ g \ cm^{-3}$,atomic mass of $Al = 27 \ g \ mol^{-1}$)

EasyMHT CET 2020

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

Similar Questions

Calculate the number of atoms in $5.4 \ g$ of a metal forming an $fcc$ structure,given that the unit cell volume $\left(a^3\right)$ multiplied by density $\left(\varrho\right)$ is $7.2 \times 10^{-22} \ g$.

Copper crystallizes in an $fcc$ lattice with a unit cell edge length of $361 \ pm$. What is the radius of the copper atom in $pm$?

If the edge length of a unit cell of $Li$ is $351 \, pm$, what is the radius of $Li$ (in $pm$)?

Ferrous oxide has a cubic structure and each edge of the unit cell is $5.0 \, \mathring{A}$. Assuming the density of the oxide is $4.0 \, g \, cm^{-3}$,the number of $Fe^{2+}$ and $O^{2-}$ ions present in each unit cell will be ($M_w$ of $FeO = 72$)

What is the number of atoms present per unit cell of aluminium having edge length $4 \ \mathring{A}$? (Given: density of $Al = 2.7 \ g \ cm^{-3}$,atomic mass of $Al = 27 \ g \ mol^{-1}$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module