gold 144 pm density 19.32 g/cm3
The radius of gold is 144 pm, and the density is 19.32 g/cm3.
Does elemental gold have a face-centered cubic structure
or a body-centered cubic structure?
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[cubic structure edge length formula]
① simple cubic (sc): a = 2r
② body-centered cubic (bcc): a = 4r / sqrt(3)
③ face-centered cubic (fcc): a = r × sqrt(8)
[단위세포에 있는 원자의 개수]
① simple cubic (sc): Z = 1
② body-centered cubic (bcc): Z = 2
③ face-centered cubic (fcc): Z = 4
( 참고 https://ywpop.tistory.com/12440 )
d = [M × Z] / [N_A × a^3]
( 참고 https://ywpop.blogspot.com/2023/09/392-pm-2145-gcm3.html )
> gold, Au의 몰질량 = 196.97 g/mol
> 1 pm = 1×10^(-10) cm 이므로,
144 pm = 144×10^(-10) cm
a와 Z를 사용해서 d를 계산해보면 된다.
[1] bcc, 체심 입방 구조일까?
a = 4r / sqrt(3)
= 4 × (144×10^(-10) cm) / sqrt(3)
= 3.3255×10^(-8) cm
d = [M × Z] / [N_A × a^3]
= [(196.97) × 2] / [(6.022×10^23) × (3.3255×10^(-8))^3]
= 17.79 g/cm3
[2] fcc, 면심 입방 구조일까?
a = r × sqrt(8)
= (144×10^(-10) cm) × sqrt(8)
= 4.073×10^(-8) cm
d = [M × Z] / [N_A × a^3]
= [(196.97) × 4] / [(6.022×10^23) × (4.073×10^(-8))^3]
= 19.36 g/cm3
≒ 19.32 g/cm3
답: face-centered cubic structure. 면심 입방 구조
[키워드] 금은 면심 입방 구조 기준, Au는 FCC 기준
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