A certain element crystallises in a bcc lattice of unit cell edge length 27 Å . If the same element under the same conditions crystallises in the fcc lattice, the edge length of the unit cell in Å will be ___________. (Round off to the nearest Integer).
[Assume each lattice point has a single atom] [Assume √3 = 1.73, √2 = 1.41]
A certain element crystallises in a bcc lattice of unit cell edge length 27 Å . If the same element under the same conditions crystallises in the fcc lattice, the edge length of the unit cell in Å will be ___________. (Round off to the nearest Integer).
[Assume each lattice point has a single atom] [Assume √3 = 1.73, √2 = 1.41]
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1 Answer
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Edge length in bcc, a? = 27 Å
Let, Edge length in fcc be a? Å
Now, the same element crystallises in bcc as well as fcc.
For bcc: 4r = √3 a? ⇒ r = (√3 / 4) a?
For fcc: 4r = √2 a? ⇒ r = a? / (2√2)
So, (√3 / 4) a? = a? / (2√2)
(√3 / 4) × 27 = a? / (2√2)
a? = 33.13 Å
The nearest integer is 33.
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