단위 세포에 있는 금속 원자의 개수

단위 세포에 있는 금속 원자의 개수

 

 

Many metals pack in cubic unit cells. The density of a metal and length of the unit cell can be used to determine the type for packing.

For example, gold has a density of 19.32 g/cm3 and a unit cell side length of 4.08 Å. (1 Å = 1×10^-8 cm.)

 

a) How many gold atoms are in exactly 1 cm3?

b) How many unit cells are in exactly 1 cm3?

c) How many gold atoms are there per unit cell?

d) The atoms/unit cell suggests that gold packs as a (i) simple, (ii) body-centered or (iii) face-centered unit cell.

 

---------------------------------------------------

 

Au의 몰질량 = 197.00 g/mol

Molar mass of Au is 197.00 g/mol

 

 

a) 5.9058×10^22 atoms

(19.32 g/cm3) / (197.00 g/mol) = 0.098071 mol/cm3 Au

(0.098071 mol/cm3) × (6.022×10^23 atoms/mol) = 5.9058×10^22 atoms/cm3

 

 

b) 1.4724×10^22 unit cells

4.08 Å = 4.08×10^-8 cm

1 cm / (4.08×10^-8 cm) = 24509803.9 (1 cm당 4.08 Å segment의 개수)

(24509803.9)^3 = 1.4724×10^22 unit cells

 

 

c) 4 atoms/unit cell

5.9058×10^22 atoms / 1.4724×10^22 unit cells = 4 atoms/unit cell

 

 

d) face-centered

simple cubic = 1 atom/unit cell

body-centered cubic = 2 atoms/unit cell

face-centered cubic = 4 atoms/unit cell

 

 

 

[키워드] 고체화학 기준문서, 단위 세포 기준문서, 단위 세포에 존재하는 금속 원자의 개수