Aluminum crystallize in cubic close packed structure with unit cell edge length of 353.6 pm.what is the radius of Al atom? How many unit cell are there is n 1.00 cm^3 of Al ?
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Given:
Aluminium crystallize in cubic close packed structure.
a = 353.6 pm = 353.6 × 10⁻¹⁰ cm
Volume of Al = 1 cm³
To Find:
The radius of Al atom and the no of unit cells in the given volume of Al.
Calculation:
- For ccp structure, we know that:
r = a / (2√2)
⇒ r = 353.6 / (2√2)
⇒ r = 125.035 pm
- Volume of 1 unit cell of Al = a³
⇒ V = (353.6 × 10⁻¹⁰)³
⇒ V = 44.212 × 10⁻²⁴ cm³
- No of unit cells = Volume of Al/Volume of 1 unit cell
⇒ N = 1/44.212 × 10⁻²⁴
⇒ N = 2.262 × 10²²
- So, the radius of Al atom is 125.035 pm and the no of unit cells in 1 cm³ of Al is 2.262 × 10²².
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