Advertisements
Advertisements
Question
The density of iridium is 22.4 g/cm3. The unit cell of iridium is fcc. Calculate the radius of iridium atom. Molar mass of iridium is 192.2 g/mol.
Advertisements
Solution
Given: Type of unit cell is fcc.
Density of iridium (ρ) = 22.4 g/cm3
Molar mass of iridium = 192.2 g/mol
To find: Radius of iridium atom (r)
Formula used:
1. Density (ρ) = `"M n"/("a"^3 "N"_"A")`
2. For fcc unit cell, r = 0.3535 a
Calculation: For fcc unit cell, n = 4, using formula (i)
Density (ρ) = `"M n"/("a"^3 "N"_"A")`
`22.4 "g cm"^-3 = (192.2 "g mol"^-1 xx 4 "atom")/("a"^3 xx 6.022 xx 10^23 "atom mol"^-1)`
`"a"^3 = (192.2 xx 4)/(22.4 xx 6.022 xx 10^23)`
a = `root(3)((192.2 xx 4)/(22.4 xx 6.022 xx 10^23))`
= `root(3)((192.2 xx 4 xx 10^-23)/(22.4 xx 6.022))`
`= root(3)((192.2 xx 40 xx 10^-24)/(22.4 xx 6.022))`
`= root(3)((192.2 xx 40 xx (10^-8)^3)/(22.4 xx 6.022))`
`= root(3)((192.2 xx 40)/(22.4 xx 6.022)) xx 10^-8`
= 3.849 × 10-8 cm
= 384.9 pm
Using formula (ii)
r = 0.3535 a
r = 0.3535 × 384.9 pm
= 135.7 pm ≈ 136 pm
Radius of iridium atom (r) is 136 pm.
RELATED QUESTIONS
Answer the following in brief.
Calculate the packing efficiency of metal crystal that has simple cubic structure.
Answer the following in brief.
Cesium chloride crystallizes in a cubic unit cell with Cl– ions at the corners and a Cs+ ion in the center of the cube. How many CsCl molecules are there in the unit cell?
Cu crystallizes in fcc unit cell with edge length of 495 pm. What is the radius of Cu atom?
In ionic crystalline solid atoms of element Y form hcp lattice. The atoms of element X occupy one-third of tetrahedral voids. What is the formula of the compound?
An element has a bcc structure with a unit cell edge length of 288 pm. How many unit cells and a number of atoms are present in 200 g of the element? (1.16 × 1024, 2.32 × 1024)
Calculate the packing efficiency for bcc lattice.
The total volume occupied by particles m simple cubic unit cell is ____________.
The number of particles in 1 g of a metallic crystal is equal to ____________.
The coordination number of each sphere in simple cubic lattice is ____________.
The percentage of vacant space of bcc unit cell is ____________.
What is the edge length of fcc type of unit cell having density and atomic mass 6.22 g cm−3 and 60 g respectively?
1 mol of CO2 contains ____________.
Atoms of elements A and B crystallize in hep lattice to form a molecule. Element A occupies 2/3 of tetrahedral voids, the formula of molecule is ______.
Copper crystallizes as face centered cubic lattice, with edge length of unit cell 361 pm. Calculate the radius of copper atom.
Copper crystallises with fee unit cell. If the radius of copper atom is 127.8 pm, calculate the density of copper? (At. mass: Cu = 63.55 g mol-1)
What is the percentage of void space in bcc type of in unit cell?
An element crystallizes in a bee lattice with cell edge of 500 pm. The density of the element is 7.5 g cm-3. How many atoms are present in 300 g of metal?
Gold crystallizes in face centred cubic structure. If atomic mass of gold is 197 g mol-1, the mass of unit cell of gold is ______.
The relation between the radius of the sphere and the edge length in the body-centred cubic lattice is given by the formula ______.
The packing efficiency of bcc is ______.
