Potassium has a BCC structure

Potassium has a BCC structure

 

 

Potassium has a BCC structure and only one atom per lattice point. The density of potassium is 0.855 g/cm^3 and the atomic weight is 39.09 g/mol. Calculate:

a. The lattice parameter and

b. The atomic radius of potassium

 

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In BCC there are 2 atoms per unit cell,

so Z for BCC = 2

 

 

d = (M × Z) / (N_A × a^3)

 

a = [(M × Z) / (N_A × d)]^(1/3) = 4/root(3) × r

 

 

d = 밀도(density). 단위: g/cm^3
M = 원자량(atomic weight). 단위: g/mol
Z = 단위세포당 원자개수(atoms per unit cell). 단위: atoms/cell 또는 atoms
N_A = 아보가드로수. 6.022×10^23 atom/mol
a = 격자인자 또는 격자상수(lattice parameter or lattice constant). 단위: cm
r = 원자반지름(atomic radius). 단위: cm

 

 

 

a = [(39.09×2) / ((6.022×10^23)×0.855)]^(1/3)

= 5.33×10^(-8) cm

= 5.33×10^(-10) m

= 5.33 Å

 

 

r = a × root(3)/4

= (5.33×10^(-8)) × root(3)/4

= 2.31×10^(-8) cm

 

 

 

[참고]

https://ocw.mit.edu/courses/materials-science-and-engineering/3-091sc-introduction-to-solid-state-chemistry-fall-2010/crystalline-materials/15-introduction-to-crystallography/MIT3_091SCF09_hw15_sol.pdf

 

 

 

[ 관련 예제 https://ywpop.tistory.com/12439 ] 392 pm 면심입방 밀도 21.45 g/cm^3

 

[ 관련 예제 https://ywpop.tistory.com/12098 ] Determine the crystal structure of the metal.

 

 

 

[키워드] 고체화학 기준문서, 입방격자 기준문서, cubic cell 기준문서

 

 

 

[ 비공개 자료 https://ywpop.tistory.com/12097 ]