The Solid State

1. Identify the given information:

- Crystal lattice type: BCC (Body-Centered Cubic)
- Unit cell edge length ( ) = 300 pm
- Density ( ) = 6.15 g cm^-3
- We need to find the Molar Mass ( ).
- We know Avogadro's number ( ) ≈ 6.022 x 10²³ mol^-1.

2. Determine the number of atoms per unit cell (Z) for BCC:

- In a BCC lattice, there is 1 atom at the body center and 1/8 of an atom at each of the 8 corners.
- atoms per unit cell.

3. Convert the unit cell edge length ( ) to cm:

- 1 pm = 10^-10 cm
-

4. Calculate the volume of the unit cell ( ):

- For a cubic cell,
-

5. Use the density formula for crystals:

- Density ( ) =
- Where:
= density
= number of atoms per unit cell
= molar mass (in g/mol)
= Avogadro's number
= volume of the unit cell

6. Rearrange the formula to solve for Molar Mass ( ):

-

7. Plug in the values and calculate :

-
-
-
-
-
-
-

Therefore, the molar mass of the metal is 50 g mol^-1.

Final Answer: The final answer is .

Let's evaluate each statement regarding defects in solids:

Frenkel defect is a vacancy defect:

• This statement is incorrect. A Frenkel defect is a type of point defect where an ion is displaced from its normal position to an interstitial site, creating a vacancy and an interstitial defect. It involves both a vacancy and an interstitial, not just a vacancy.

Schottky defect is a dislocation defect:

• This statement is incorrect. A Schottky defect is a point defect where a pair of ions (typically cations and anions) are missing from the crystal lattice, leading to vacancies. It is not a dislocation defect.

Trapping of an electron in the lattice leads to the formation of F-centre:

• This statement is correct. An F-centre is a point defect where an electron is trapped in a vacancy within the lattice, causing the lattice to absorb light and give a characteristic color. This occurs due to the presence of trapped electrons.

Schottky defect has no effect on density:

• This statement is incorrect. A Schottky defect causes a loss of ions (both cations and anions), which leads to a decrease in the density of the material.

The correct answer is (C) : Trapping of an electron in the lattice leads to the formation of F-centre.

Step 1: Convert the Metallic Radius to Meters

The metallic radius is given in Å (angstroms). We need to convert it to meters:

Step 2: Calculate the Edge Length of the Unit Cell

In a BCC lattice, the edge length of the unit cell can be related to the atomic radius by the formula: Substituting the given radius:

Step 3: Calculate the Volume of the Unit Cell

The volume of a cubic unit cell is given by: Substituting the edge length:

Conclusion

The volume of the unit cell is . The closest option to this value is: Therefore, the correct answer is (C) 6.4 × 10^-29.

Let's match the types of crystalline solids (Column A) with suitable examples (Column B):

Detailed Explanation:

• Molecular Solid (P):
  • Example: H₂O (ice), molecules held by intermolecular hydrogen bonds (van der Waals forces).
• Ionic Solid (Q):
  • Example: MgO (magnesium oxide), ions held by electrostatic forces.
• Metallic Solid (R):
  • Example: Mg (magnesium metal), metal atoms surrounded by a "sea of electrons".
• Network Solid (S):
  • Example: SiC (silicon carbide), atoms connected by covalent bonds in an extensive network.

Matched pairs:

• P → H₂O (iii)
• Q → MgO (iv)
• R → Mg (ii)
• S → SiC (i)

Conclusion:

The correct matched set is:

P-iv, Q-iii, R-ii, S-i, which corresponds to Option (B).

Correct Answer: Option (B)

1. Simple cubic (SC):

Atoms touch along the edges.

Therefore, radius for SC:

1. Body-centered cubic (BCC):

Atoms touch along the body diagonal of the cube.

Therefore, radius for BCC:

1. Face-centered cubic (FCC):

Atoms touch along the face diagonal.

Therefore, radius for FCC:

Combining these results:

Simple cubic : Body-centered cubic : Face-centered cubic

Conclusion:

The correct ratio is:

Correct Answer: Option (B)

To solve the problem of calculating the number of atoms in a given mass of a face-centred cubic (FCC) crystal, we need to follow a series of steps involving understanding the crystal structure and performing some calculations.

1. Identify the unit cell type: The crystal is face-centred cubic (FCC).
2. Determine the number of atoms per unit cell in FCC:
3. Understand the relation between edge length and atomic radius for FCC:
4. Calculate the volume of 4.5 g of the crystal:
5. Convert mass to moles:
6. Calculate the total number of atoms:
7. Conclusion:

To conclude, the problem involves understanding FCC structure, using geometric relations in cubic cells, converting given mass into mole with respect to atomic weight, and finally applying Avogadro's number for the total atom count.