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Cubic unit cells: packing efficiency and density

37 questions on Cubic unit cells: packing efficiency and density from the Solid State chapter: 8 NEET level, 16 JEE Main, 13 JEE Advanced. Each one opens with its answer and solution.

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The packing efficiency of a simple cubic unit cell is nearest to NEET level
For a face-centred cubic unit cell of atoms of radius r, the edge length a is NEET level
A crystal has N atoms in a ccp arrangement. The number of octahedral voids in it is NEET level
The percentage of space occupied by atoms in a bcc structure is about NEET level
Copper crystallises in a face-centred cubic lattice with edge length 360 pm. Taking M = 63.5 g mol^-1 and N_A = 6.022x10^23 mol^-1, calculate the density of cop... JEE Main level
A metal crystallises in a body-centred cubic lattice with unit cell edge 330 pm. Using sqrt3 = 1.732, calculate the atomic radius in pm (nearest integer). JEE Main level
A cubic metal of molar mass 52 g mol^-1 has unit cell edge 288 pm and density 7.23 g cm^-3. Using N_A = 6.022x10^23 mol^-1, find the number of atoms per unit ce... JEE Main level
Rock salt, NaCl (M=58.5 g mol^-1), has an fcc arrangement of ions with 4 formula units per unit cell and density 2.165 g cm^-3. With N_A = 6.022x10^23 mol^-1, c... JEE Main level
Which of the following are correct for a hexagonal close packed (hcp) arrangement of identical spheres? JEE Main level
The correct increasing order of packing efficiency is JEE Main level
In a cubic unit cell, atoms P occupy all 8 corners except one, atoms Q occupy the centres of all 6 faces and atoms R occupy the body centre. The simplest formul... JEE Main level
In rock salt the ions touch along the cell edge. If the unit cell edge is 564 pm and the radius of Cl- is 181 pm, the radius of Na+ is JEE Main level
CsCl has a cubic cell with Cs+ at the body centre and Cl- at the corners, the ions touching along the body diagonal. Taking r(Cs+)=169 pm, r(Cl-)=181 pm, M=168.... JEE Advanced level
In rock salt (4 formula units per cell) the Na+ and Cl- ions touch along the cell edge. With r(Na+)=100 pm, r(Cl-)=181 pm and pi=3.14, find the percentage of th... JEE Advanced level
An fcc metal has density 10.5 g cm^-3 and unit cell edge 409 pm. Using N_A=6.022x10^23 mol^-1, calculate its molar mass in g mol^-1 (nearest integer). JEE Advanced level
Iron transforms from fcc (a=364 pm) to bcc (a=285 pm) on cooling, the unit cell edges being measured at the same temperature for the two forms. Find the ratio r... JEE Advanced level
A metal (M=63.5 g mol^-1) with atomic radius 128 pm crystallises in a fcc lattice. Take sqrt2=1.414, N_A=6.022x10^23 mol^-1. Which statements are correct? JEE Advanced level
Three metals X (simple cubic), Y (bcc) and Z (fcc) have the same atomic radius and the same atomic mass. Which statements about their densities are correct? JEE Advanced level
An element crystallises in an fcc lattice with unit cell edge 4.00x10^-8 cm and density 10.0 g cm^-3. The number of atoms in 100 g of the element is JEE Advanced level
What is the packing efficiency of a body-centred cubic (bcc) lattice of identical atoms? NEET level
How many atoms belong to one face-centred cubic (fcc) unit cell? NEET level
For atoms of radius r in a bcc lattice, the edge length a is related to r by NEET level
What is the coordination number of an atom in a simple cubic lattice? NEET level
A metal of atomic mass 64 g mol^-1 crystallises in a face-centred cubic lattice with edge length 360 pm. Its density in g cm^-3 is (take N_A = 6.022 x 10^23 mol... JEE Main level
A metal crystallises in an fcc lattice and its atomic radius is 128 pm. Taking sqrt2=1.414, the edge length of the unit cell in pm is JEE Main level
Iron is bcc with edge length 287 pm in one of its forms. Taking sqrt3=1.732, the radius of an iron atom in pm is JEE Main level
A cubic ionic solid of formula mass 58.5 g mol^-1 has edge length 564 pm and density 2.16 g cm^-3. Using N_A = 6.022x10^23 mol^-1, the number of formula units p... JEE Main level
Copper crystallises in an fcc lattice with edge length 361 pm. Taking the atomic mass of Cu as 63.5 and N_A = 6.022x10^23 mol^-1, calculate the density in g cm^... JEE Main level
Sodium (atomic mass 23) is bcc and has density 0.97 g cm^-3. Using N_A = 6.022x10^23 mol^-1, find the edge length of its unit cell in pm (nearest integer). JEE Main level
Silver is fcc with edge length 409 pm and density 10.5 g cm^-3. Using N_A = 6.022x10^23 mol^-1, calculate its atomic mass (nearest integer, in g mol^-1). JEE Main level
Which of the following statements about a bcc lattice of identical atoms are correct? JEE Main level
An element exists in an fcc form and in a bcc form. Assume the atomic radius is the same in both forms. Taking sqrt2=1.414 and sqrt3=1.732, the ratio rho_fcc/rh... JEE Advanced level
A bcc metal has atomic mass 56 g mol^-1. Using N_A = 6.022x10^23 mol^-1, the number of unit cells present in 10.0 g of the metal is JEE Advanced level
In a CsCl-type crystal the ions touch along the body diagonal of the cubic cell. Take r(Cs^+)=169 pm, r(Cl^-)=181 pm, sqrt3=1.732, atomic masses Cs =133, Cl =35... JEE Advanced level
A metal of atomic mass 108 crystallises in an fcc lattice and has density 10.4 g cm^-3. Using N_A=6.022x10^23 mol^-1 and sqrt2=1.414, find the atomic radius in ... JEE Advanced level
Which of the following statements about a face-centred cubic lattice of identical atoms (radius r, edge a) are correct? JEE Advanced level
Atoms of the same radius r are packed in simple cubic (sc), bcc and fcc arrangements. Which statements about the cell volume per atom are correct? JEE Advanced level