Elemental magnesium crystallizes in a face-centered cubic lattice. The density o

Question

Elemental magnesium crystallizes in a face-centered cubic lattice. The density of magnesium is 1.738 g/cm. The unit cell length is 4.80 × 102 pm. What is the atomic radius of Mg? A) 340 pm B) 215 pm C) 242 pnm D) 126 pnm E) 170 pm ANS: E KEY: general chemistry | phases | solid | calculations with unit cell dimensions PTS: 1 DIF: difficult TOP: 16.4 Chromium metal crystallizes as a body-centered cubic lattice. If the atomic radius of Cr is 1.25 angstroms, what is the density of Cr metal in grams per cubic centimeter? A) 2.76 g/cm3 B) 5.52 g/cm C) 7.18 g/cm D) 3.59 g/cm E) 7.81 g/cm PTS: 1 DIF: difficult TOP: 16.4 ANS: C KEY: general chemistry | phases |solid| calculations with unit cell dimensions

Explanation / Answer

1)
for FCC
length of face diagonal = 4*r
a*sqrt(2) = 4*r
480 pm * 1.4142 = 4*r
r = 170 pm
Answer: 170 pm

2)
Here r = 1.25 A
r = 1.25*10^-8 cm

length of body diagonal = sqrt(a^2+a^2+a^2)
length of body diagonal = a*sqrt(3)

use:
For BCC Lattice
length of body diagonal = 4*r
a*sqrt(3) = 4*r

Given: r = 1.25*10^-8 cm
So,
a = 4*r/(sqrt(3))
a = 4*1.25*10^-8/(sqrt(3)) cm
a = 2.887*10^-8 cm

Molar mass = 52.0 g/mol
since the cubic cell is Body Centred Cubic, the value of Z=2

d = (Z*M)/(a^3*NA)
d = (2*52)/((2.887*10^-8)^3*(6.022*10^23))
d = 7.18 g/cm^3
Answer: 7.18 g/cm^3

Related Questions

Navigate

• Browse (All)
• Browse E
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.