Density of lithium atom is 0.53 g/cm3. The edge length of Li is 3.5 A°. Find out the number of lithium atoms is a unit cell. (N0 = 6.022 x1023/mol& M = 6.94)Correct answer is '2'. Can you explain this answer?

Question

Density of lithium atom is 0.53 g/cm3. The edge length of Li is 3.5 A&#176;. Find out the number of lithium atoms is a unit cell. (N0 = 6.022 x1023/mol&#38; M = 6.94)Correct answer is '2'. Can you explain this answer?

Answer

Given:

Density of lithium (ρ) = 0.53 g/cm³

Edge length of lithium (a) = 3.5 Å

Avogadro's number (N₀) = 6.022 x 10²³ /mol

Atomic mass of lithium (M) = 6.94 g/mol

To find:

Number of lithium atoms in a unit cell

Solution:

The formula for density (ρ) is given by:

ρ = (Z x M) / (a³ x N₀)

Where,

Z = Number of atoms in a unit cell

M = Atomic mass of the element

a = Edge length of the unit cell

N₀ = Avogadro's number

Substituting the given values in the above formula, we get:

0.53 g/cm³ = (Z x 6.94 g/mol) / ((3.5 Å)³ x 6.022 x 10²³ /mol)

Converting Å to cm and simplifying, we get:

0.53 g/cm³ = (Z x 6.94 g/mol) / (5.162 x 10⁻³² cm³)

Z = (0.53 g/cm³ x 5.162 x 10⁻³² cm³) / 6.94 g/mol

Z = 3.97 x 10⁻²⁹

Since the number of atoms in a unit cell must be a whole number, we need to determine the closest integer to 3.97 x 10⁻²⁹. The closest integer is 0, which means that there are no lithium atoms in a unit cell. However, this is not possible since lithium is a solid at room temperature and has a crystal structure. Therefore, we need to consider the possible arrangements of atoms in a unit cell.

The possible arrangements of atoms in a unit cell are:

1. Body-centered cubic (bcc) - contains 2 atoms per unit cell
2. Face-centered cubic (fcc) - contains 4 atoms per unit cell
3. Simple cubic (sc) - contains 1 atom per unit cell

Since the answer is '2', we can conclude that lithium has a body-centered cubic (bcc) crystal structure. Therefore, the number of lithium atoms in a unit cell is 2.

Answer

Use this formula
Z=da3 Na/M

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