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Aluminium crystallizes in a cubic close-packed structure with a unit cell edge length of 353.6 pm. What is the radius of Al atom? How many unit cells are there in 1.00 cm3 of Al? - Chemistry

Sum

Aluminium crystallizes in a cubic close-packed structure with a unit cell edge length of 353.6 pm. What is the radius of Al atom? How many unit cells are there in 1.00 cm3 of Al? 

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Solution

Given: Type of unit cell is ccp.
Edge length (a) = 353.6 pm = 3.536 × 10–8 cm Volume (V) of Al = 1.00 cm3

To find:

1. Radius of Al atom (r)

2. Number of unit cells in 1.00 cm3 of Al

Formulae:

1. For ccp (fcc) unit cell, r = 0.3535 a

2. Number of unit cells in volume (V) of metal = `"V"/"a"^3`

Calculation:

1. Using formula (i),

r = 0.3535 a

∴ r = 0.3535 × 353.6 = 125 pm

2. Using formula (ii),

Number of unit cells in volume (V) of metal = `"V"/"a"^3`

∴  Number of unit cells in 1.00 cm3 of Al = `(1.00)/(3.536 xx 10^-8)^3 = 2.26 xx 10^22`

1. Radius of Al atom (r) is 125 pm.

2. Number of unit cells in 1.00 cm3 of Al is 2.26 × 1022.

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Balbharati Chemistry 12th Standard HSC for Maharashtra State Board
Chapter 1 Solid State
Exercise | Q 5 | Page 27
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