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.
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 one or two sentences.
Which of the three types of packing used by metals makes the most efficient use of space and which makes the least efficient use?
Answer the following in one or two sentences.
Mention two properties that are common to both hcp and ccp lattices.
Answer the following in brief.
Calculate the packing efficiency of metal crystal that has simple cubic structure.
Cu crystallizes in fcc unit cell with edge length of 495 pm. What is the radius of Cu atom?
Aluminium crystallizes in a cubic close-packed structure with a unit cell edge length of 353.6 pm. What is the radius of Al atom? How many unit cells are there in 1.00 cm3 of Al?
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?
Calculate the packing efficiency for bcc lattice.
In case of hcp structure, how are spheres in first, second and third layers arranged?
A substance crystallizes in fcc structure. The unit cell edge length is 367.8 pm. Calculate the molar mass of the substance if its density is 21.5 g/cm3.
Identify the INCORRECT match.
A compound of X and Y crystallizes in ccp structure in which the X atoms occupy the lattice points at the corners of cube and Y atoms occupy the centres of each of the cube faces. The formula of this compound is ____________.
The vacant space in simple cubic lattice is ____________.
Which of the following contains the highest number of atoms?
Which among the following crystal structures the edge length of unit cell is equal to twice the radius of one atom?
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?
Which of the following is INCORRECT?
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?
AB is an ionic solid. If the ratio of ionic radius of A+ and B- is 0.52, what is the coordination number of B- ?
Calculate packing efficiency in face-centred cubic lattice.
A compound made of elements C and D crystallizes in a fee structure. Atoms of C are present at the corners of the cube. Atoms of D are at the centres of the faces of the cube. What is the formula of the compound?
The packing efficiency of bcc is ______.
