Question

The density of iridium is \(22.4\) g cm\({}^{-3}\). The unit cell of iridium is fcc Calculate the volume of unit cell. if the molar mass of iridium is \(192.2\) g/mol.

• A. \(5.7\times 10^{-23}\) cm\({}^{3}\)
• B. \(2.8\times 10^{-23}\) cm\({}^{3}\)
• C. \(3.1\times 10^{-23}\) cm\({}^{3}\)
• D. \(4.6\times 10^{-23}\) cm\({}^{3}\)

Hint:

Use density equals Z times molar mass divided by volume times Avogadro's number, with Z = 4 for fcc.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept
Density of a crystal is \(\rho=\dfrac{ZM}{N_A\,V}\), where \(V\) is the volume of the unit cell. For fcc, \(Z=4\).

Step 2: Rearrange
\(V=\dfrac{ZM}{\rho N_A}\).

Step 3: Calculation
\(V=\dfrac{4\times 192.2}{22.4\times 6.022\times 10^{23}}=\dfrac{768.8}{1.349\times 10^{25}}=5.7\times 10^{-23}\ \text{cm}^3\).

Final Answer:
The volume of the unit cell is 5.7 times 10 to the power minus 23 cubic centimetres, which is option (A). \[ \boxed{\text{(A) }5.7\times 10^{-23}\text{ cm}^{3}} \]