Physics Chapter 12 Quiz

The energy levels of a particle in an infinite potential well, where the particle is a muon (µ).

The wave functions of a particle in an infinite potential well, where the particle is a muon (µ).

A phenomenon where light interference patterns are observed due to the interaction of light reflected between a flat surface and a curved lens.

The minimum distance between the flat surface and the lens in a Newton's Rings experiment to observe a bright central fringe.

A material that exhibits different refractive indices for light polarized along different axes.

The minimum thickness of a retarding plate required to ensure that linearly polarized light emerges linearly polarized, regardless of the angle of incidence.

The amplitude of the magnetic field associated with a laser beam, expressed in terms of the permittivity of free space (𝜀0) and the speed of light (𝑐).

The boundary between two dielectric media with different permittivities, where there is no free charge present.

The phenomenon where the wavelength of a photon increases when it collides with a charged particle, such as an electron, and transfers some of its energy to the particle.

The maximum change in wavelength (Δλ) during Compton Scattering occurs when the scattered photon travels in the opposite direction to the incident photon (θ = 180°).

The maximum possible wavelength of the scattered photon (λ') in Compton scattering occurs when the scattered photon has lost the most energy. This happens at the maximum scattering angle (θ = 180°).

The energy of a particle in a parabolic trajectory around a planet is always positive. This indicates that the particle is not bound to the planet and has enough energy to escape its gravitational pull.

The angular momentum (L) of a particle in a parabolic trajectory around a planet is a constant value, calculated using the mass (m), gravitational constant (G), planet's mass (M), and the distance of closest approach (rm).

The motion of an object where the damping force is so strong that the object returns to equilibrium with the least possible oscillations. It has no overshooting and settles quickly.

The motion of an object where the damping force is smaller than that required for critical damping. The object oscillates with decreasing amplitude before settling at equilibrium.

The motion of an object where the damping force is so weak that the object oscillates back and forth with a decreasing amplitude. It takes a long time to settle at equilibrium.

The component of the velocity of the source (𝑣(𝑡)) along the line joining the source and the observer (P).

The frequency observed by an observer due to the motion of the source. It can vary based on the source's position and velocity.

The frequency observed when the source is at the maximum displacement from its equilibrium position (𝑥 = ±𝑎).

The frequency observed when the source is passing through its equilibrium position (𝑥 = 0).

The work done by the system when one mole of an ideal monoatomic gas expands isothermally from 𝑉𝑜 to 2.5𝑉𝑜.

The change in internal energy of the system when one mole of an ideal monoatomic gas expands isothermally from 𝑉𝑜 to 2.5𝑉𝑜.

The work done by the system when one mole of an ideal monoatomic gas expands isobarically from 𝑉𝑜 to 2.5𝑉𝑜.

The change in internal energy of the system when one mole of an ideal monoatomic gas expands isobarically from 𝑉𝑜 to 2.5𝑉𝑜.

The total charge induced on the inner surface of a spherical shell made of a linear dielectric material with a relative permittivity of 9, when a charge of -9C is placed at its center, is -8C. This is calculated using the concept of dielectric polarization and Gauss's law.

The voltage drop across the 2kΩ resistor in the circuit with a Zener diode (10V, 2W) and a normal diode (0.7V turn-on) is 9.3V. This is calculated by analyzing the circuit and considering the operating conditions of the diodes.

The energy of a level in a system with Fermi energy 5.5eV, having a probability of occupancy of 0.2 at 500K, is approximately 5.66eV. This is calculated using the Fermi-Dirac distribution function and considering the temperature and Fermi energy.

The net change in entropy of one mole of an ideal monoatomic gas heated from 273K to 303K and then from 303K to 373K is approximately 0.69R. This is calculated using the formula for entropy change of an ideal gas undergoing an isothermal process.

The smallest inter-planar spacing d that can be determined from the second order of diffraction of a simple cubic crystal using X-rays of wavelength 1.32Å is 0.66Å. This is calculated using Bragg's law and considering the order of diffraction.

The collector current IC in the transistor circuit is 10 mA. This is calculated using the transistor parameters (β = 100, VBE = 0.7V) and applying Kirchhoff's laws to analyze the circuit.

A Hermitian matrix is a square matrix that is equal to its Hermitian conjugate. It is a matrix that is equal to its own complex conjugate transpose.

A unitary matrix is a square matrix whose inverse is equal to its conjugate transpose.

The matrix given in choice (B) is Hermitian. This is because a matrix and its conjugate transpose are equal. However, the square of this matrix is not the identity matrix. So, the matrix is not unitary.

Therefore, the correct answer is (B).

The divergence of a vector field is a measure of how much the field is expanding or contracting at a given point.

The divergence of the vector field 𝑟̂/𝑟³ is given by the formula:

div (𝑟̂/𝑟³) = ∇ . (𝑟̂/𝑟³) = (1/𝑟²) d/dr (𝑟² (1/𝑟³)) = -1/𝑟⁴ .

Therefore, the correct answer is (A).

The spin magnetic moment of a particle is a measure of its intrinsic angular momentum, which is a fundamental property of particles. It's related to the spin, which is a form of angular momentum that doesn't involve the particle's motion around a point.

Electrons, protons, and neutrons all have spin magnetic moments, but their magnitudes differ notably:

• Electrons have the strongest spin magnetic moment (μe).
• Protons have a weaker spin magnetic moment (μp).
• Neutrons, although neutral overall, have a small but non-zero spin magnetic moment (μn).

Therefore, the correct answer is (A).

The NaCl crystal, also known as table salt, has a face-centered cubic (FCC) lattice structure. In the NaCl crystal, the Na+ and Cl- ions occupy alternate positions within the cubic lattice. Think of it as layers of ions alternating between Na+ and Cl- ions.

Each unit cell of the FCC lattice has 4 lattice points. Since each lattice point is occupied by an ion, a unit cell of NaCl contains 4 Na+ and 4 Cl- ions. Thus, there are a total of 8 ions per unit cell.

The probability density describes the likelihood of finding a particle at a given location at a specific time. In this scenario, the particle approaches x=0 from x=-∞. The probability density P(x) goes to zero as x approaches negative infinity. This shows that the wave function of the particle approaches zero as x approaches negative infinity. The particle is not present in the region of x < -∞, but after passing through the potential barrier the probability density is non-zero in the region x > 0.

Binary numbers are made up of only two digits, 0 and 1. Decimal numbers are the familiar system we use every day, with digits 0-9.

To convert a binary number to decimal, you assign each digit a power of 2, starting from 2⁰ for the rightmost digit and increasing to the left. The decimal equivalent is the sum of these products.

For example, 10110.10 in binary is equivalent to: (1 × 2⁴) + (0 × 2³) + (1 × 2²) + (1 × 2¹) + (0 × 2⁰) + (1 × 2⁻¹) + (0 × 2⁻²) = 16 + 4 + 2 + 0.5 = 22.5

You can apply the same process to the other binary numbers and add their decimal equivalents together to find the final decimal value.

The sum of three binary numbers: 10110.10, 11010.01, and 10101.11. You have to convert each of these numbers into their decimal form and add the results. You can use the following formula: Decimal equivalent = (2^n * bn) + (2^(n-1) * b(n-1)) + ... + (2^0 * b0) + (2^-1 * b-1) + (2^-2 * b-2) + ... Where: bi = ith digit in the binary number, n = the position of the leftmost digit (counting from 0 from right to left) and i = the position of the digit in the binary number.

A path integral represents the work done by an electric field along a specific path. It's calculated by integrating the dot product of the electric field and the infinitesimal displacement along the path.

The induced electric field is a consequence of a changing magnetic field. It's created to oppose the change in magnetic flux. Faraday's law quantifies this relationship.

A solenoid is a long coil of wire that creates a uniform magnetic field inside. When the current in the solenoid changes, the magnetic field also changes, inducing an electric field.

The amplitude of the induced electric field is directly proportional to the rate of change of the magnetic field. The strength of the induced electric field is increased with a faster-changing magnetic field.

The electric field is a vector quantity representing the force exerted on a unit positive charge at a given point. It's directed from higher potential to lower potential.