The Solid State

Al = 2.7 g/cm3, Ge = 5.323 g/cm3, Si = 2.33 g/cm3.
The densities of aluminum (Al), germanium (Ge), and silicon (Si) are as follows:

Aluminum (Al): The density of aluminum is approximately 2.70 grams per cubic centimeter (g/cm³).

Germanium (Ge): The density of germanium is around 5.32 grams per cubic centimeter (g/cm³).

Silicon (Si): The density of silicon is about 2.33 grams per cubic centimeter (g/cm³).

Please note that these values are approximate and can vary based on factors such as temperature and pressure.

In the powder diffraction pattern of a crystalline solid, the graph typically represents the diffraction angles and the intensity of diffracted rays. The variables in this graph are:
Step 1: The x-axis represents the angle , which is the angle of diffraction. This angle is related to the scattering angle in X-ray diffraction experiments.
Step 2: The y-axis represents the intensity of the diffracted rays, which shows the intensity of the peaks corresponding to specific diffraction angles.
Step 3: Thus, the correct variables for the powder diffraction pattern are: .

Step 1: Understanding the Classification of Colloidal Systems
- Aerosols (A) are colloidal dispersions of solid or liquid particles in a gas, such as smoke (IV).
- Foams (B) are gas dispersed in a liquid, like soap lather (II).
- Emulsions (C) are liquid-liquid colloidal dispersions, such as milk (I).
- Gels (D) are semi-solid colloidal systems where liquid is dispersed in a solid, like cheese (III).
Step 2: Verifying the Matches - A = IV (Smoke) - B = II (Soap lather) - C = I (Milk) - D = III (Cheese)
Final Answer: The correct matching is Option D.

The electron configuration of lanthanides follows a general pattern, where the electrons fill the 4f, 5d, and 6s orbitals. The given configuration is [Xe] 4f⁵ 5d¹ 6s².
- The electron configuration for (Cerium) is [Xe] 4f¹ 5d¹ 6s², so it matches the required configuration.
- The electron configuration for (Gadolinium) is [Xe] 4f⁷ 5d¹ 6s², which also matches the required configuration, with the exception of the 4f electrons.
- The electron configuration for (Lutetium) is [Xe] 4f¹ 5d¹ 6s², matching the required configuration.
Thus, the lanthanides Ce, Gd, and Lu have the configuration [Xe] 4f⁵ 5d¹ 6s² in their ground state.

Chemisorption refers to the process where the adsorbate forms strong chemical bonds with the adsorbent.
It involves a single layer of adsorbate and is generally specific to the adsorbent. The key characteristics of chemisorption are:
Step 1: Unlike physisorption (which is multilayered), chemisorption involves a single layer of adsorption. Therefore, statement (1) is incorrect.
Step 2: Chemisorption is not typically reversible, as the bonds formed are strong. Therefore, statement (2) is incorrect.
Step 3: Chemisorption is highly specific in nature, as it involves the formation of chemical bonds. Thus, statement (3) is incorrect.
Step 4: The enthalpy of adsorption for chemisorption typically lies in the range of 80-240 kJ/mol, which is consistent with the high energy of bond formation in this process. Thus, statement (4) is correct.

Analysis of CCP Lattice in Compound X₃Y₂

The number of atoms in the CCP lattice is n.

• The number of octahedral voids is n.
• The number of tetrahedral voids is 2n.

In the given compound X₃Y₂, Y forms the CCP lattice. Therefore, the number of Y atoms is:

n = 2.

• The number of octahedral voids is 2.
• The number of tetrahedral voids is 4.

The X atoms occupy 50% of the octahedral voids. Therefore, the number of X atoms in octahedral voids is:

0.5 × 2 = 1.

Let the number of X atoms in tetrahedral voids be a. The total number of X atoms is 3. Hence, we have:

1 + a = 3, which means a = 2.

The percentage of tetrahedral voids occupied by X atoms is:

.

The percentage of unoccupied tetrahedral voids is:

100 - 50 = 50%.

Coal gasification refers to the process of converting coal into a gaseous mixture known as "coal gas" by reacting it with water vapor at high temperatures. The main chemical reaction involved in coal gasification is the conversion of carbon (in coal) with steam to produce carbon monoxide and hydrogen. The reaction can be written as: This reaction takes place at high temperatures (typically around 1270 K), which leads to the formation of CO and H2 gases.
This is the correct reaction for coal gasification.

BOD (Biochemical Oxygen Demand) is a measure of the amount of oxygen required by microorganisms to decompose organic matter in water. In pure water, the BOD value is low, typically less than 5 ppm, as it contains fewer organic pollutants. For highly polluted water, the BOD value is high, typically greater than 17 ppm, because of the increased amount of organic material present.
Step 1: For pure water, the BOD is generally less than 5 ppm. For highly polluted water, the BOD is generally greater than 17 ppm.
Step 2: Thus, the correct relationship between the BOD values for pure and highly polluted water is .

Carrots are a rich source of vitamin A, which is essential for maintaining healthy vision and immune function. Curd (yogurt) is a good source of vitamin B12, which is important for nerve function and the formation of red blood cells.
- Carrots are well known for being high in vitamin A.
- Curd is rich in vitamin B12, especially for vegetarians, as B12 is primarily found in animal products.
Thus, the correct vitamins are A for carrot and B12 for curd, making option (1) the correct answer.

To determine the correctness of the statements provided, let's analyze each statement one by one:

Statement I: Viscosity of liquid decreases with increase in temperature.

As temperature increases, the kinetic energy of the molecules in a liquid increases, causing them to move more rapidly. This increased movement reduces the cohesive forces among the molecules, leading to a decrease in viscosity. Therefore, Statement I is correct.

Statement II: The units of viscosity coefficient are Pascal sec.

The viscosity coefficient is often measured in units of Pascal seconds (Pa·s). This is derived from the equation for dynamic viscosity, which is the ratio of shear stress (in Pascals) to shear rate (in sec⁻¹). Hence, Statement II is also correct.

Both statements are validated by the scientific principles of fluid dynamics and the units of physical measurements. Therefore, the correct answer is: Both statement-I and statement-II are correct.

Terylene is a polyester formed by the polymerization of terephthalic acid and ethylene glycol. Glyptal is a polymer made from phthalic acid and ethylene glycol. Both of these polymers share ethylene glycol (HO-CH₂-CH₂-OH) as the common monomer.
Step 1: Terylene is formed by the reaction between terephthalic acid (a benzene ring with two carboxyl groups) and ethylene glycol. Glyptal is made from phthalic acid (a benzene ring with a carboxyl group) and ethylene glycol.
Step 2: The common monomer for both Terylene and Glyptal is ethylene glycol, which has the structure HO-CH₂-CH₂-OH. Thus, the correct answer is option (1) HO-CH₂-CH₂-OH.

Given:

• Crystal structure: fcc (Face-Centered Cubic)
• Edge length,
• Density,
• Mass of metal sample,

Step 1: Calculate the volume of one unit cell ( ): Step 2: Calculate the mass of one unit cell ( ) using the density formula: . Step 3: Calculate the number of unit cells present in 0.015 kg of metal: The number of unit cells present in 0.015 kg of the metal is .
Correct Answer: (3)