Work Energy And Power

Step 1: Understanding Resonance in a Column of Air In a resonance column, resonance occurs at the positions of the odd harmonics of the fundamental mode. The resonance depths follow the pattern: where corresponds to the th harmonic.
Step 2: Finding the Wavelength Given: The difference between successive resonance depths gives half of the wavelength:
Step 3: Determining the Third Resonance Depth The third resonance depth is given by:

According to the given figure, X is at a lower potential with respect to Y. Hence, both diodes are in reverse biasing, so the equivalent circuit can be redrawn as follows: 

Equivalent Resistance Calculation: 

Step 1: Understanding the Forbidden Energy Gap The forbidden energy gap (also known as the band gap) is the energy difference between the valence band and the conduction band in a solid material. It determines the electrical conductivity of a material.
Step 2: Classification of Materials Based on Band Gap - Conductors ( eV): No band gap; electrons move freely. - Semiconductors ( eV): Small band gap; thermal energy can excite electrons. - Insulators ( eV, typically around 5 eV): Large band gap; electrons cannot easily transition to the conduction band.
Step 3: Correct Option For an insulator, the band gap is typically greater than 3 eV, and in most cases, it is around 5 eV. Hence, the correct option is:

Step 1: Understanding Frenkel and Schottky defects. Frenkel and Schottky defects are two types of point defects that occur in crystalline solids.
- Schottky Defect:
- Occurs in ionic solids (e.g., NaCl, KCl).
- Equal number of cations and anions are missing from the crystal lattice.
- Results in a decrease in density of the crystal.
- Frenkel Defect:
- Occurs in ionic solids with large size differences between cations and anions (e.g., AgCl, ZnS). - A cation moves from its normal position to an interstitial site.
- Does not affect density.
Step 2: Identifying the correct classification. - These defects occur within the crystal structure, hence they are crystal defects. - They are not related to the nucleus or non-crystalline materials.
Final Answer:

Step 1: Formula for energy densities in an electromagnetic wave. The total energy density in an electromagnetic wave is the sum of the electric and magnetic energy densities. The electric energy density and magnetic energy density are given by: where is the permittivity of free space, is the permeability of free space, is the electric field, and is the magnetic field.
Step 2: Relationship between electric and magnetic fields. In an electromagnetic wave, the energy density is equally distributed between the electric and magnetic fields, so:
Step 3: Total energy density. The total energy density is the sum of the electric and magnetic energy densities: Step 4: Ratio of average electric energy density to total energy density. The ratio is: Thus, the ratio of average electric energy density to total average energy density is .

To find the maximum kinetic energy of the emitted photoelectrons, we use the photoelectric equation: , where is the maximum kinetic energy, is the energy of the incoming photon, and is the work function of the metal.
Step 1: Calculate
The energy of a photon can be calculated using the equation , where , , and .

Convert this energy to electron volts (eV) using the conversion :

Step 2: Calculate
Given , the maximum kinetic energy is:

Since the closest option is 1.1 eV, the maximum kinetic energy of the emitted photoelectrons is approximately 1.1 eV.