Answer to Question #90200 in Physical Chemistry for Anant sahu
2019-05-24T13:58:31-04:00
If carbon-carbon Bond length in diamond is 1.5 angstorm then what will be the edge length of the cubic closed packed unit cell of diamond having alternate tetrahedral voids occupied?
1
2019-05-27T06:09:48-0400
Given:
r c − c = 1.5 A n g s t r o m r_{c-c} = 1.5 { \ \ Angstrom } r c − c = 1.5 A n g s t ro m Solution :
CCP cell:
From triangle ABC:
A B = r c − c AB= r_{c-c} A B = r c − c A C = ( A B ) 2 2 AC= \sqrt{\frac{(AB)^2}{2} } A C = 2 ( A B ) 2 Edge length is:
L = 2 ∗ A C = 2 ∗ ( A C ) 2 2 = 2 ( A C ) 2 = 2 r c − c 2 L = 2 * AC = 2 * \sqrt{\frac{(AC)^2}{2}} = \sqrt{2(AC)^2} = \sqrt{2r_{c-c}^2} L = 2 ∗ A C = 2 ∗ 2 ( A C ) 2 = 2 ( A C ) 2 = 2 r c − c 2 Calculating:
L = 2 r c − c 2 = 2 ∗ 1. 5 2 ≈ 2.12 A n g s t r o m L =\sqrt{2r_{c-c}^2} = \sqrt{2*1.5^2}\approx 2.12 \ Angstrom L = 2 r c − c 2 = 2 ∗ 1. 5 2 ≈ 2.12 A n g s t ro m Answer: 2.12 Angstrom
References:
https://hemantmore.org/chemistry-1/c11201018/1899/
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