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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. - Chemistry

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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.

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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)

Formulae: 
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)/(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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Balbharati Chemistry 12th Standard HSC for Maharashtra State Board
Chapter 1 Solid State
Exercise | Q 4 | Page 27
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