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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.
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