Question

Aluminium ystallizes in Cubic close packed strie
Jure with unit ceul edge length of 353.5 F
What is the readius of Alatom? How many
unts cell are there in 1.00 cm of AIZ​

Answer 1

Question:

Aluminium crystallizes in cubic close packed structure with unit cell edge length of 353.5 pm. What is the radius of Al atom? How many unit cells are there in 1 cm³ of Al ?

Answer:

Radius = 125 pm

Number of unit cells = 2.268 × 10²²

Explanation:

Given:

• Structure of aluminium atom = Cubic Close packed structure (ccp)
• Length of cell edge = 353.5 pm

To Find:

• Radius of Al atom
• Number of unit cells in 1 cm³ of Al atom

Solution:

The radius of an atom in a ccp structure is given by,

a = 2√2 r

where a is the edge length and r is the radius

Substitute the data,

353.5 = 2√2 r

r = 353.5/2 × 1.414

r = 353.5/2.828

r = 125 pm

Hence the radius of the Al atom is 125 pm.

Now number of unit cells in 1 cm³ is given by,

Number of unit cells = Volume/Volume of each each cell

Number of unit cells = 1/a³

⇒ 1 cm³/(353.4 × 10⁻¹⁰cm)³

⇒ 1/ (4.41 × 10⁻²³)

⇒ 0.2268 × 10²³

⇒ 2.2268 × 10²²

Hence 2.268 × 10²² number of unit cells are present.

Answer 2

$\huge \bf Given :-$

Edge = 353.5 F

Unit ce = 1.00 cm

$\huge \bf To \: Find :-$

Radius

Total cell

$\huge \bf Solution$

As we know that

a = 2√2r

353.5 = 2√2r

r = 353.5/2 × 1.414

r = 125 pm

Now,

Unit cells = 1/a³

1/(353.5 × 10^-10)

Now,

Unit cell = 2.26 × 10²²