The Solid State

Step 1: Concept
Metallic bonding is best described by the "Electron Sea Model".
Step 2: Analysis
In this model, a lattice of positive ions (kernels) is immersed in a "sea" of mobile valence electrons.
Step 3: Conclusion
These electrons move freely throughout the metallic crystal boundaries.
Final Answer: (A)

Step 1: Concept
The coordination number is determined by the radius ratio ( ).
Step 2: Analysis
The radius ratio . This value lies between 0.414 and 0.732.
Step 3: Conclusion
For a radius ratio in this range, the coordination number is 6.
Final Answer: (B)

Step 1: Concept
The coordination number is determined by the radius ratio ( ).
Step 2: Analysis
The radius ratio . This value lies between 0.414 and 0.732.
Step 3: Conclusion
For a radius ratio in this range, the coordination number is 6.
Final Answer: (B)

Step 1: Concept
Cubic close packing (CCP) follows the a-b-c-a-b-c pattern.
Step 2: Analysis
Sodium chloride ( ) has a face-centered cubic (FCC) arrangement.
Step 3: Conclusion
FCC is equivalent to CCP, which uses the a-b-c-a-b-c stacking sequence.
Final Answer: (C)

Step 1: Concept
Metallic bonding is best described by the "Electron Sea Model".
Step 2: Analysis
In this model, a lattice of positive ions (kernels) is immersed in a "sea" of mobile valence electrons.
Step 3: Conclusion
These electrons move freely throughout the metallic crystal boundaries.
Final Answer: (A)

Step 1: Bond Order
The bond order for both and is calculated to be .
Step 2: Electron Configuration
has the configuration . has the configuration .
Step 3: Stability Analysis
Although the bond orders are the same, is less stable than because it contains an electron in the antibonding molecular orbital ( ), which increases repulsion and decreases stability.
Final Answer: (d)

Step 1: Torque Concept
Torque ( ) required to move the door remains constant: .
Step 2: Initial Torque
.
Step 3: New Force
For , N.
Final Answer: (d)

Step 1: Concept
For an ideal transformer, the ratio of currents is inversely proportional to the turns ratio: .
Step 2: Analysis
Given and .
.
Step 3: Conclusion
The primary current .
Final Answer: (A)

Step 1: Equivalent Capacitance
The 4 µF and 2 µF capacitors are in parallel, giving . This combination is in series with the 6 µF capacitor. The equivalent capacitance is .
Step 2: Total Charge
Total charge in the circuit .
Step 3: Branch Charge
In parallel, charge divides proportionally to capacitance. For the 4 µF branch: .
Final Answer: (c)

Step 1: Given Values
. The galvanometer current .
Step 2: Shunt Formula
The voltage across the galvanometer and shunt are equal: .
Step 3: Calculation
.
Final Answer: (a)

Step 1: Concept
Packing fraction is the ratio of the volume occupied by particles to the total volume of the unit cell.
Step 2: Formula
For a diamond cubic structure, the packing efficiency is given by the formula:
Step 3: Calculation

Step 4: Conclusion
The maximum proportion of volume filled is 0.34 or 34%.
Final Answer: (B)

Concept: Density relation: Number of unit cells

Step 1: Convert volume:


Step 2: Find volume of one unit cell using density relation:
For NaCl structure, Molar mass of KBr:

Step 3: Calculate number of unit cells:
Conclusion:
Number of unit cells

Step 1: Understanding the Concept:
Silicates are classified based on the arrangement of SiO tetrahedra. Chain silicates (pyroxenes) have a structure where two oxygen atoms per tetrahedron are shared.

Step 2: Detailed Explanation:
In chain silicates (inosilicates), each SiO tetrahedron shares two of its oxygen atoms with neighboring tetrahedra, forming long chains. The general formula for a single-chain silicate is (SiO ) . This can also be written as (Si O ) , which simplifies to SiO per unit.
• (A) (Si O ) : Correct formula for chain silicates (e.g., pyroxenes). • (B) (Si O ) : Incorrect. • (C) Si O : This is a discrete anion (pyrosilicate), found in sorosilicates. • (D) Si O : This is also a discrete anion, found in sorosilicates.

Step 3: Final Answer:
The anion present in chain silicates is (Si O ) , which corresponds to option (A).

Concept: NaCl structure is face-centered cubic.

Step 1: Correct relations.

• Coordination number =
• Radius ratio = to
• Structure = fcc

Step 2: Edge length relation.
Correct formula: Conclusion: Option (C) is incorrect.