Question

A metal has a simple cubic lattice. The edge length of the unit cell is 400pm. If the molar mass of the metal is 64g mol^-1 , then the approximate density of the unit cell is ​

Answer 1

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Explanation:

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Answer 2

Given:

The metal forms a simple cubic structure.

a = 400 pm = 4 × 10⁻⁸ cm

Molar mass of metal = 64 gm

To Find:

The density (d) of the unit cell of metal.

Calculation:

- NA = 6.022 × 10²³

- For simple cubic structure, z = 1

- V = a³ = (4 × 10⁻⁸)³

⇒ V = 64 × 10⁻²⁴ cm³

- We know the formula:

V × NA × d = z × M

⇒ d = (z × M)/(V × NA)

⇒ d = (1 × 64)/(64 × 10⁻²⁴ × 6.022 × 10²³)

⇒ d = 1 / (6.022 × 10⁻¹)

⇒ d = 1.66 gm/cm³ ≈ 1.7 gm/cm³

- So, the correct option is (a) 1.7 gm/cm³.