Applied Physics
- What is the difference between direct band gap and indirect band gap semiconductors? In one line In a direct band gap semiconductor the conduction band minimum and valence band maximum occur at the same crystal momentum k , s... 1
- How is the electrical conductivity of an intrinsic and extrinsic semiconductor expressed? In one line The conductivity of a semiconductor is σ = e(nμ_e + pμ_h) , the sum of contributions from electrons and holes; for intrinsic mat... 1
- What is drift velocity of charge carriers and how is it related to current? In one line Drift velocity is the small average velocity that free electrons (or holes) acquire in the direction set by an applied electric... 1
- What is mobility of charge carriers and what factors affect it? In one line Mobility is the drift velocity acquired by a charge carrier per unit electric field, μ = v_d/E , and it measures how easily carr... 1
- How is the electrical conductivity of a metallic conductor derived in terms of drift velocity and mobility? In one line In a metal the current density is J = nev_d = neμ E , so conductivity is σ = neμ = ne²τ/m , set by the free-electron density and... 1
- What is the Fermi-Dirac distribution function and how does it behave at different temperatures? In one line The Fermi-Dirac distribution function f(E) = 1/(1 + e^((E - E_F)/kT)) gives the probability that an electron energy state E is o... 1
- Why does the Fermi level lie at the middle of the band gap in an intrinsic semiconductor? In one line In an intrinsic semiconductor the number of electrons in the conduction band equals the number of holes in the valence band, and... 1
- Where does the Fermi level lie in n-type and p-type extrinsic semiconductors, and why? In one line In an n-type semiconductor the Fermi level lies close to the conduction band (between the donor level and E_c at 0 K), and in a... 1
- How does the Fermi level in extrinsic semiconductors shift with temperature and doping concentration? In one line As temperature rises, the Fermi level of both n-type and p-type semiconductors moves towards the middle of the gap (the material... 1
- What does the Gauss divergence theorem state and how is it used in electrodynamics? In one line The divergence theorem states that the total outward flux of a vector field through a closed surface equals the volume integral... 1
- What does Stokes' theorem state and how is it used to derive Maxwell's curl equations? In one line Stokes' theorem states that the line integral of a vector field around a closed loop equals the surface integral of its curl ove... 1
- What are Maxwell's equations in point (differential) form and how are they derived? In one line Maxwell's four equations in point form are nabla·D = ρ , nabla·B = 0 , nabla×E = -∂B/∂ t and nabla×H = J + ∂D/∂ t , describing e... 1
- What are Maxwell's equations in integral form and what does each one mean physically? In one line In integral form, Maxwell's equations relate the flux of D and B through closed surfaces, and the circulation of E and H around... 1
- Why are Maxwell's equations significant and what is the role of displacement current? In one line Maxwell's equations unify electricity, magnetism and light into one theory, and Maxwell's displacement current term made them co... 1
- What is de Broglie's hypothesis of matter waves and why was it proposed? In one line De Broglie proposed that every moving particle has a wave associated with it, with wavelength λ = h/p , just as light waves show... 1
- 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