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Question

Aluminum crystallizes in a cubic close-packed structure. Its metallic radius is 125 pm. (i) What is the length of the side of the unit cell? (ii) How many unit cells are there in 1.00cm3 of aluminum?


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Solution

Step 1: Given data

The radius of the metal is 125pm

Volume of Aluminium given is 1.00cm3

Step 2: Calculating the length

We know that for closed-packed structures:

a=22ra=22×125a=354pm

Step 3: Calculating the number of unit cell

As we have the radius (r) as 125pm and the length (a) as 354pm

Volumeofunitcell=a3V=354pm3V=4.4×10-23cm3[1pm=10-10cm]

Number of unit cells in 1.00cm3 of aluminium is:

1.004.4×10-23=2.27×1022

Therefore, length of the side of the unit cell is 354 pm and Number of unit cells in 1.00cm3 of aluminium is 2.27×1022


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