QUESTION: Manganese has a density of 7.33 g/cm^3 and unit cell edge length of 3.68 Å. Calculate the atomic radius (in Å) of manganese.

Chemistry & Chemical Reactivity
9th Edition
ISBN:9781133949640
Author:John C. Kotz, Paul M. Treichel, John Townsend, David Treichel
Publisher:John C. Kotz, Paul M. Treichel, John Townsend, David Treichel
Chapter12: The Solid State
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QUESTION: Manganese has a density of 7.33 g/cm^3 and unit cell edge length of 3.68 Å. Calculate the atomic radius (in Å) of manganese.

*Please use the pictures provided (the formula and some values that can be substituted

P:
nA
VCNA
Where: p density (g/cm³)
n = no. of atoms/ unit cell
A = atomic weight (g/mol)
Important
conversion factors
1 cm = 107 nm
1 cm = 10¹⁰ pm
1 cm = 10⁰ Å
1 nm = 10 Å
Vc = volume / unit cell (cm³/unit cell) = a³
NA = Avogadro's number = 6.022x10²3 atoms/mol
Transcribed Image Text:P: nA VCNA Where: p density (g/cm³) n = no. of atoms/ unit cell A = atomic weight (g/mol) Important conversion factors 1 cm = 107 nm 1 cm = 10¹⁰ pm 1 cm = 10⁰ Å 1 nm = 10 Å Vc = volume / unit cell (cm³/unit cell) = a³ NA = Avogadro's number = 6.022x10²3 atoms/mol
Coordination number
Number of atoms per
unit cell
APF (%)
Relationship of r and a
SC
6
1
52
r =
1
2
α
BCC
8
2
68
r =
√3
4
a
FCC
12
4
74
r =
√2
4
a
Transcribed Image Text:Coordination number Number of atoms per unit cell APF (%) Relationship of r and a SC 6 1 52 r = 1 2 α BCC 8 2 68 r = √3 4 a FCC 12 4 74 r = √2 4 a
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