A metal having a cubic structure has a density of 1.892 g/cm3

A metal having a cubic structure has a density of 1.892 g/cm3

 

 

A metal having a cubic structure has a density of 1.892 g/cm^3, an atomic weight of 132.91 g/mol, and a lattice parameter of 6.13 Å. One atom is associated with each lattice point. Determine the crystal structure of the metal.

 

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d = (M × Z) / (N_A × a^3)

 

1.892 = (132.91 × Z) / ((6.022×10^23) × (6.13×10^(-8))^3)

Z = 1.892 × ((6.022×10^23) × (6.13×10^(-8))^3) / 132.91

= 1.97 ≒ 2

---> BCC

 

 

 

 

 

[ 관련 예제 https://ywpop.tistory.com/12096 ] Potassium has a BCC structure.

 

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

 

 

 

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