gold 144 pm density 19.32 g/cm3

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