Question

Compute the number of atoms per unit cell of copper crystals

Answer 1

Answer:

Solution :

The weight of one mole of a substance is equal to its atomic mass in grams , therefore

1 mole of Al =27g of Aluminium

Also , 1 mole contains Avogadro number of atoms :-1mole=6.023×10²³ atoms of Aluminium

Therefore , 1 mole of Al - 27 g of aluminium - 6.023×10²³ atoms of aluminium

Number of atoms in 8.1g aluminium is =(8.1×6.023×10²³)/27

The face centered cubic structure contains 4 atoms in one unit cell .

Therefore , the number of unit cells that has (8.1×6.023×10²³)/27 atoms of Aluminium can be obtained as ,

(8.1×6.023×10²³)/(27×4)=4.516×10²²

Answer 2

$\huge\underline\orange{Answer}$

$\large{\boxed{{Mass\:Of\:Unit\:Cell=4.22×{10}^{-22}}}}$

$\huge\underline\orange{Solution}$

In face centered cubic arrangement face diagonal is four times the radius of atoms face diagonal

$\large{=>4×128}$

$\large{\boxed{Face\: diagonal ={\sqrt{2} × edge length}}}$

Edge Length :-

$\large{Edge\:Lenght=>{\frac{512}{{\sqrt{2}}}}}$

$\large\red{Edge\:Lenght =362×{10}^{-10}cm}$

Volume of the unit cell

$\large{{(362×{10}^{-10})}^{3}}$

$\large\red{47.4×{10}^{24}{cm}^{3}}$

In a face centered cubic unit cell, there are four atoms per unit cell

Mass of unit cell

$\large{4×{\frac{4×63.5}{6.023×{10}^{23}}}}$

$\large\blue{\boxed{Mass\:Of\:Unit\: Cell=4.22×{10}^{-22}}}$

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