hromium has a body centered cubic crystal structure. If the density of chromium is 7.14g/cm³, what is he radius of the chromium atom? olution se the density and the mass of the chromium atom to find the volume of the unit cell and the unit cell ength. M D = V here are two atoms inside the body centered cubic unit cell. The mass of two atoms, in grams, is -24 g = 1.727 × 10-22 g (1.66054 × 10* 2(52.00 ати) 1 ати

Chemistry: Principles and Practice
3rd Edition
ISBN:9780534420123
Author:Daniel L. Reger, Scott R. Goode, David W. Ball, Edward Mercer
Publisher:Daniel L. Reger, Scott R. Goode, David W. Ball, Edward Mercer
Chapter11: Liquids And Solids
Section: Chapter Questions
Problem 11.78QE
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I am very confused as to where you got the 1.272 x 10-22 from 

Chromium has a body centered cubic crystal structure. If the density of chromium is 7.14g/cm³, what is
the radius of the chromium atom?
Solution
Use the density and the mass of the chromium atom to find the volume of the unit cell and the unit cell
length.
M
D =
V
There are two atoms inside the body centered cubic unit cell. The mass of two atoms, in grams, is
1.66054 × 10-24
2(52.00 ати)
= 1.727 × 10-22 a
1 ати
Use the density and the mass to find the volume of a unit cell and the length of one side.
1.272 × 10–22
M
V =
D
g
= 1.78 x 10-23
7.14
ст3
a = VV = V1.78 × 10-23cm³
= 2.9 x 10-8cm = 2.9 Å
%3D
Then use the Pythagorean Theorem to find the radius.
(4r)? = a² + (v2a)´ = a² + 2a² = 3a²
= V3a
4r =
V3
(2.9 × 10-10 m) = 1.3 × 10-10 m
4
r =
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Transcribed Image Text:Chromium has a body centered cubic crystal structure. If the density of chromium is 7.14g/cm³, what is the radius of the chromium atom? Solution Use the density and the mass of the chromium atom to find the volume of the unit cell and the unit cell length. M D = V There are two atoms inside the body centered cubic unit cell. The mass of two atoms, in grams, is 1.66054 × 10-24 2(52.00 ати) = 1.727 × 10-22 a 1 ати Use the density and the mass to find the volume of a unit cell and the length of one side. 1.272 × 10–22 M V = D g = 1.78 x 10-23 7.14 ст3 a = VV = V1.78 × 10-23cm³ = 2.9 x 10-8cm = 2.9 Å %3D Then use the Pythagorean Theorem to find the radius. (4r)? = a² + (v2a)´ = a² + 2a² = 3a² = V3a 4r = V3 (2.9 × 10-10 m) = 1.3 × 10-10 m 4 r = We've updated our Give it a
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