First Year (FE)
- How is the de Broglie wavelength of an electron accelerated through a potential difference V derived? In one line An electron accelerated from rest through a potential difference V gains kinetic energy eV , so its de Broglie wavelength is λ =... 1
- What are the main properties of matter waves and how do they differ from light waves? In one line Matter waves are probability waves associated with moving particles; their wavelength is h/mv , they are not electromagnetic, an... 1
- What is a wave function and what does its probability density tell us about a particle? In one line The wave function psi is a mathematical function that describes the quantum state of a particle, and |psi|² gives the probabilit... 1
- What mathematical conditions must a wave function satisfy to be physically acceptable? In one line A physically acceptable (well-behaved) wave function must be single-valued, finite, continuous, have a continuous first derivati... 1
- How do you solve numerical problems on de Broglie wavelength for electrons and other particles? In one line Pick the right form of λ = h/p for the given data (speed, kinetic energy or accelerating voltage), substitute constants in SI un... 1
- Why was Schrödinger's equation needed and what is its significance in quantum mechanics? In one line Schrödinger's equation was needed because classical mechanics could not describe the wave behaviour of particles; it is the basi... 1
- How is Schrödinger's time-independent wave equation derived for a particle in one dimension? In one line Starting from the classical wave equation and substituting de Broglie's λ = h/p with p² = 2m(E - V) , we get d²psi/dx² + 8π²m/h²... 1
- How is the energy of a particle trapped in a one-dimensional rigid box derived using Schrödinger's equation? In one line Solving Schrödinger's equation for a particle confined between two infinitely high walls a distance L apart gives quantised ener... 1
- How is Schrödinger's time-dependent wave equation derived and what are the energy and momentum operators? In one line Differentiating the free-particle wave function Psi = Ae^(-i(Et - px)/hbar) gives the operators E → ihbar ∂/∂ t and p → -ihbar ∂... 1
- How do you solve numerical problems on the energy of a particle in a rigid box? In one line Use E_n = n²h²/(8mL²) in SI units for the required level, and use Δ E = E_(n_2) - E_(n_1) with λ = hc/Δ E for transitions betwee... 1
- What is quantum mechanical tunnelling and how can a particle cross a barrier higher than its energy? In one line Quantum tunnelling is the effect in which a particle has a non-zero probability of passing through a potential barrier even when... 1
- What is a qubit and how is it different from a classical bit in quantum computing? In one line A qubit is the basic unit of quantum information that can exist in a superposition of the states |0rangle and |1rangle at the sa... 1
- What is the gradient of a scalar field and what is its physical meaning? In one line The gradient of a scalar field is a vector that points in the direction in which the field increases fastest, and its magnitude... 1
- What is the divergence of a vector field and what does it tell us physically? In one line Divergence of a vector field measures the net outward flow (flux) per unit volume from a point, showing whether the point acts a... 1
- What is the curl of a vector field and what is its physical significance? In one line Curl of a vector field is a vector that measures how much the field circulates or rotates around a point, with direction along t... 1
- What does Gauss's law of electrostatics state and how is its point form obtained? In one line Gauss's law states that the total electric flux through any closed surface equals the net charge enclosed divided by ε₀ ; in poi... 1
- What is Ampere's circuital law and how is it written in differential (point) form? In one line Ampere's circuital law states that the line integral of magnetic field around any closed loop equals μ₀ times the net current pa... 1
- What does Faraday's law of electromagnetic induction state and what is its point form? In one line Faraday's law states that the emf induced in a closed loop equals the negative rate of change of magnetic flux through it; in po... 1
- What is the critical angle and when does total internal reflection of light take place? In one line The critical angle is the angle of incidence in the denser medium for which the refracted ray just grazes the boundary, and for... 1
- How does light propagate through an optical fibre by total internal reflection? In one line An optical fibre guides light because its core has a higher refractive index than its cladding, so light entering within the acc... 1
- What are the acceptance angle and acceptance cone of an optical fibre? In one line The acceptance angle is the maximum angle to the fibre axis at which light can enter the fibre and still be guided by total inte... 1
- What is the numerical aperture of an optical fibre and how is its formula derived? In one line Numerical aperture (NA) is the sine of the acceptance angle (times the index of the outside medium) and measures how much light... 1
- What is the difference between single-mode and multimode optical fibres? In one line A single-mode fibre has a very thin core that lets only one path (mode) of light travel, while a multimode fibre has a thicker c... 1
- How do step-index and graded-index optical fibres differ in structure and light travel? In one line In a step-index fibre the core has one uniform refractive index that drops suddenly at the cladding, while in a graded-index fib... 1