Physics

01 PHY-LEARN-001 What CSS Physics Tests +

Physics requires conceptual understanding, mathematical formulation, derivation, numerical problem-solving, diagrams and physical interpretation across both 100-mark papers.

02 PHY-LEARN-002 Paper-I and Paper-II Map +

Paper-I covers mechanics, fluids, waves/optics and thermodynamics/statistical physics; Paper-II covers electromagnetism, modern/quantum physics, solid-state physics and nuclear/particle physics.

03 PHY-LEARN-003 SI Units and Dimensional Analysis +

Use coherent SI units, dimensions and consistency checks to detect algebraic and numerical errors.

04 PHY-LEARN-004 Significant Figures and Scientific Notation +

Report numerical results with appropriate precision and powers of ten.

05 PHY-LEARN-005 Scalars and Vectors +

Distinguish magnitude-only quantities from quantities requiring magnitude and direction.

06 PHY-LEARN-006 Vector Components and Unit Vectors +

Resolve vectors into orthogonal components and reconstruct magnitude and direction.

07 PHY-LEARN-007 Dot Product +

Use scalar product for projection, work and angular relationships.

08 PHY-LEARN-008 Cross Product +

Use vector product for torque, angular momentum and oriented area.

09 PHY-LEARN-009 Scalar Triple Product +

Interpret the triple product geometrically and apply it to volume and vector identities.

10 PHY-LEARN-010 Vector Triple Product +

Use standard expansion identities carefully and verify ordering.

11 PHY-LEARN-011 Gradient +

Interpret gradient as direction and rate of maximum increase of a scalar field.

12 PHY-LEARN-012 Divergence +

Interpret divergence as local source/sink strength of a vector field.

13 PHY-LEARN-013 Curl +

Interpret curl as local circulation or rotational tendency of a vector field.

14 PHY-LEARN-014 Divergence Theorem +

Relate volume divergence to flux through a closed surface.

15 PHY-LEARN-015 Stokes' Theorem +

Relate surface curl to circulation around a boundary.

16 PHY-LEARN-016 Calculus for Physics +

Use differentiation and integration as descriptions of local rate and accumulated physical quantity.

17 PHY-LEARN-017 Differential Equations in Physics +

Recognize first- and second-order equations and connect mathematical solutions to initial/boundary conditions.

18 PHY-LEARN-018 Approximation and Limiting Cases +

Test formulas in simple limits and identify when an approximation is physically justified.

19 PHY-LEARN-019 Graphical Reasoning +

Extract slope, area, intercept, asymptotic behavior and physical trends from graphs.

20 PHY-LEARN-020 Numerical Answer Protocol +

Write given data, governing equation, substitution with units, calculation and physical interpretation.

21 PHY-LEARN-021 Kinematics in One Dimension +

Derive displacement, velocity and acceleration relations using calculus rather than relying only on constant-acceleration formulas.

22 PHY-LEARN-022 Kinematics in Two and Three Dimensions +

Represent position, velocity and acceleration as vectors and resolve motion component-wise.

23 PHY-LEARN-023 Projectile Motion +

Analyze ideal projectile motion and state assumptions such as uniform gravity and negligible drag.

24 PHY-LEARN-024 Relative Motion +

Transform velocities and positions between classical inertial frames.

25 PHY-LEARN-025 Newton's First Law +

Understand inertia and the role of inertial frames.

26 PHY-LEARN-026 Newton's Second Law +

Apply the vector relation between net force and rate of change of momentum.

27 PHY-LEARN-027 Newton's Third Law +

Identify action-reaction pairs acting on different bodies.

28 PHY-LEARN-028 Free-Body Diagrams +

Isolate a body and display only external forces before writing equations of motion.

29 PHY-LEARN-029 Friction +

Distinguish static and kinetic friction and apply limiting-friction conditions correctly.

30 PHY-LEARN-030 Work +

Calculate work as the line integral of force along displacement.

31 PHY-LEARN-031 Kinetic Energy +

Derive and apply the work-energy theorem.

32 PHY-LEARN-032 Potential Energy +

Relate conservative force to potential-energy gradients.

33 PHY-LEARN-033 Conservation of Mechanical Energy +

Apply energy conservation where non-conservative work is absent or separately accounted for.

34 PHY-LEARN-034 Power +

Relate rate of doing work to force and velocity.

35 PHY-LEARN-035 Linear Momentum +

Define momentum and connect net external force to momentum change.

36 PHY-LEARN-036 Impulse +

Relate impulse to change in momentum.

37 PHY-LEARN-037 Conservation of Linear Momentum +

Apply momentum conservation to isolated systems and collisions.

38 PHY-LEARN-038 Center of Mass +

Calculate center-of-mass position and motion for particle systems.

39 PHY-LEARN-039 Elastic and Inelastic Collisions +

Use momentum and energy conditions to distinguish collision classes.

40 PHY-LEARN-040 Angular Position, Velocity and Acceleration +

Develop rotational kinematics as the angular analogue of translational motion.

41 PHY-LEARN-041 Torque +

Relate force and lever arm to rotational effect.

42 PHY-LEARN-042 Angular Momentum +

Define orbital angular momentum and apply conservation under zero external torque.

43 PHY-LEARN-043 Moment of Inertia +

Calculate rotational inertia and interpret dependence on mass distribution.

44 PHY-LEARN-044 Parallel- and Perpendicular-Axis Theorems +

Use axis theorems to obtain moments of inertia for shifted or related axes.

45 PHY-LEARN-045 Rotational Kinetic Energy +

Relate angular speed and moment of inertia to kinetic energy.

46 PHY-LEARN-046 Rigid-Body Dynamics +

Apply torque equations to rotational motion of extended bodies.

47 PHY-LEARN-047 Rolling Motion +

Combine translation and rotation under rolling-without-slipping constraints.

48 PHY-LEARN-048 Spin and Precession +

Understand angular-momentum response to applied torque.

49 PHY-LEARN-049 Gyroscope +

Analyze gyroscopic precession conceptually and quantitatively at syllabus level.

50 PHY-LEARN-050 Universal Gravitation +

Apply Newton's inverse-square gravitational law.

51 PHY-LEARN-051 Gravitational Field +

Define field strength and use superposition.

52 PHY-LEARN-052 Gravitational Potential +

Relate potential, potential energy and gravitational field.

53 PHY-LEARN-053 Escape Speed +

Derive escape speed from energy conservation.

54 PHY-LEARN-054 Orbital Motion +

Relate gravitational force to circular orbital dynamics.

55 PHY-LEARN-055 Satellite Energy +

Derive kinetic, potential and total energy for circular orbits.

56 PHY-LEARN-056 Kepler's First Law +

Understand elliptical planetary orbits with the central body at a focus.

57 PHY-LEARN-057 Kepler's Second Law +

Relate equal areas in equal times to angular-momentum conservation.

58 PHY-LEARN-058 Kepler's Third Law +

Relate orbital period to orbital size for gravitational systems.

59 PHY-LEARN-059 Centripetal Force +

Recognize centripetal force as the net inward force required for curved motion, not a new fundamental force.

60 PHY-LEARN-060 Classical Relativity and Its Limits +

Understand Galilean transformations and why electromagnetism motivated a revised spacetime framework.

61 PHY-LEARN-061 Michelson-Morley Experiment +

Understand the experimental motivation and null result historically without treating it as the sole basis of relativity.

62 PHY-LEARN-062 Einstein's First Postulate +

Apply equivalence of physical laws in inertial frames.

63 PHY-LEARN-063 Einstein's Second Postulate +

Understand invariance of the vacuum speed of light for inertial observers.

64 PHY-LEARN-064 Lorentz Transformations +

Transform space and time coordinates between inertial frames.

65 PHY-LEARN-065 Relativity of Simultaneity +

Understand frame dependence of simultaneity.

66 PHY-LEARN-066 Time Dilation +

Derive and apply the relation between proper and coordinate time.

67 PHY-LEARN-067 Length Contraction +

Derive and apply contraction along the direction of relative motion.

68 PHY-LEARN-068 Relativistic Velocity Transformation +

Combine velocities consistently with Lorentz transformations.

69 PHY-LEARN-069 Relativistic Momentum +

Understand momentum's relativistic form and classical limit.

70 PHY-LEARN-070 Relativistic Energy +

Relate total energy, rest energy and kinetic energy.

71 PHY-LEARN-071 Mass-Energy Equivalence +

Interpret E=mc² as rest-energy equivalence and use the full energy-momentum relation.

72 PHY-LEARN-072 Energy-Momentum Relation +

Apply E²=p²c²+m²c⁴ and examine massless and low-speed limits.

73 PHY-LEARN-073 Relativity Numerical Strategy +

Identify proper quantities, frames and Lorentz factor before substitution.

74 PHY-LEARN-074 Density and Pressure +

Relate mass density, force and area to fluid pressure.

75 PHY-LEARN-075 Hydrostatic Pressure +

Derive pressure variation with depth in a fluid at rest.

76 PHY-LEARN-076 Pascal's Principle +

Apply pressure transmission in confined fluids.

77 PHY-LEARN-077 Buoyancy and Archimedes' Principle +

Relate buoyant force to displaced-fluid weight.

78 PHY-LEARN-078 Surface Tension +

Understand surface energy and force per unit length.

79 PHY-LEARN-079 Capillarity +

Relate surface tension, contact angle and tube radius to capillary rise/depression.

80 PHY-LEARN-080 Viscosity +

Understand internal resistance to shear and velocity gradients.

81 PHY-LEARN-081 Poiseuille Flow +

Analyze laminar flow through a cylindrical tube and parameter dependence.

82 PHY-LEARN-082 Stokes' Law +

Apply viscous drag on a sphere in the low-Reynolds-number regime.

83 PHY-LEARN-083 Terminal Velocity +

Balance forces to determine terminal speed in a viscous medium.

84 PHY-LEARN-084 Elastic Stress and Strain +

Define normal/shear stress and corresponding strain.

85 PHY-LEARN-085 Hooke's Law +

Apply linear elastic proportionality within the elastic limit.

86 PHY-LEARN-086 Elastic Moduli +

Distinguish Young's, bulk and shear moduli.

87 PHY-LEARN-087 Continuity Equation for Fluids +

Apply mass conservation to steady flow.

88 PHY-LEARN-088 Bernoulli's Theorem +

Derive and apply energy conservation along a streamline under stated assumptions.

89 PHY-LEARN-089 Bernoulli Applications +

Analyze flow speed, pressure and height in idealized fluid systems.

90 PHY-LEARN-090 Reynolds Number +

Interpret the dimensionless ratio governing laminar/turbulent tendencies.

91 PHY-LEARN-091 Fluid Problem Assumptions +

State incompressibility, steady flow, negligible viscosity or other assumptions before applying ideal-fluid formulas.

92 PHY-LEARN-092 Simple Harmonic Motion +

Derive SHM from a restoring force proportional to displacement.

93 PHY-LEARN-093 SHM Energy +

Track kinetic, potential and total energy through an oscillation.

94 PHY-LEARN-094 SHM Phase +

Relate displacement, velocity and acceleration phases.

95 PHY-LEARN-095 Simple Pendulum +

Derive the small-angle period and state approximation limits.

96 PHY-LEARN-096 Physical Pendulum +

Relate rotational inertia and restoring torque to period.

97 PHY-LEARN-097 One-Degree-of-Freedom Free Oscillation +

Solve the basic undamped oscillator equation with initial conditions.

98 PHY-LEARN-098 Two Coupled Oscillators +

Understand coupled equations and energy exchange.

99 PHY-LEARN-099 Normal Modes +

Find characteristic collective motions of coupled systems.

100 PHY-LEARN-100 Damped Oscillation +

Distinguish underdamped, critically damped and overdamped motion.

101 PHY-LEARN-101 Forced Oscillation +

Analyze steady response to periodic driving.

102 PHY-LEARN-102 Resonance +

Understand amplitude enhancement near natural frequency and the role of damping.

103 PHY-LEARN-103 Quality Factor +

Relate damping, resonance sharpness and stored/dissipated energy.

104 PHY-LEARN-104 Traveling Waves +

Represent propagation using wave functions and phase.

105 PHY-LEARN-105 Wave Equation +

Derive and interpret the classical wave equation.

106 PHY-LEARN-106 Wave Speed +

Relate propagation speed to medium properties.

107 PHY-LEARN-107 Energy Transmission by Waves +

Understand energy flux and dependence on amplitude/frequency.

108 PHY-LEARN-108 Phase Velocity +

Define speed of a constant phase.

109 PHY-LEARN-109 Group Velocity +

Define envelope speed and its relation to energy/information in appropriate media.

110 PHY-LEARN-110 Dispersion +

Understand frequency-dependent phase velocity.

111 PHY-LEARN-111 Standing Waves +

Derive standing waves from superposition of counter-propagating waves.

112 PHY-LEARN-112 Nodes and Antinodes +

Locate zero- and maximum-amplitude points.

113 PHY-LEARN-113 Strings and Normal Frequencies +

Apply boundary conditions to stretched strings.

114 PHY-LEARN-114 Sound Waves +

Understand longitudinal pressure/density disturbances.

115 PHY-LEARN-115 Sound Intensity +

Relate power per area to amplitude and acoustic energy.

116 PHY-LEARN-116 Beats +

Explain amplitude modulation from nearby frequencies.

117 PHY-LEARN-117 Doppler Effect +

Analyze observed frequency shifts due to relative source-observer motion.

118 PHY-LEARN-118 Wave Problem Strategy +

Identify propagation direction, phase convention, boundary conditions and requested physical quantity.

119 PHY-LEARN-119 Reflection +

Apply the law of reflection and wavefront reasoning.

120 PHY-LEARN-120 Refraction +

Apply Snell's law and refractive index.

121 PHY-LEARN-121 Total Internal Reflection +

Derive the critical-angle condition and identify applications.

122 PHY-LEARN-122 Interference +

Use superposition and phase difference to determine constructive/destructive interference.

123 PHY-LEARN-123 Young's Double-Slit Interference +

Derive fringe spacing and conditions.

124 PHY-LEARN-124 Thin-Film Interference +

Account for optical path and phase reversals.

125 PHY-LEARN-125 Interferometers +

Understand interference-based precision measurement at syllabus level.

126 PHY-LEARN-126 Michelson Interferometer +

Analyze path difference and fringe shifts.

127 PHY-LEARN-127 Newton's Rings +

Derive ring conditions and use them for wavelength/refractive measurements.

128 PHY-LEARN-128 Diffraction +

Distinguish diffraction from geometrical spreading and interference.

129 PHY-LEARN-129 Single-Slit Fraunhofer Diffraction +

Derive minima and interpret the intensity pattern.

130 PHY-LEARN-130 Double-Slit Diffraction and Interference +

Combine diffraction envelope with interference fringes.

131 PHY-LEARN-131 Diffraction Grating +

Derive principal maxima and grating equation.

132 PHY-LEARN-132 Resolving Power of a Grating +

Understand resolution and its dependence on order and illuminated lines.

133 PHY-LEARN-133 Spectrometer +

Understand angular measurement and spectral analysis principles.

134 PHY-LEARN-134 Polarization +

Understand polarization as evidence of transverse wave character.

135 PHY-LEARN-135 Malus' Law +

Relate transmitted intensity to analyzer angle.

136 PHY-LEARN-136 Brewster's Law +

Relate polarizing angle to refractive index.

137 PHY-LEARN-137 Electromagnetic Wave Equation +

Derive the wave equation from Maxwell-type field relations at an appropriate level.

138 PHY-LEARN-138 Normal Dispersion +

Understand ordinary variation of refractive index with frequency away from resonance.

139 PHY-LEARN-139 Anomalous Dispersion +

Understand reversed dispersion behavior near absorption regions.

140 PHY-LEARN-140 Coherence +

Distinguish temporal and spatial coherence and their role in interference.

141 PHY-LEARN-141 Laser Principles +

Understand stimulated emission, population inversion, resonator and coherent output.

142 PHY-LEARN-142 Laser Characteristics +

Explain monochromaticity, directionality, coherence and high intensity.

143 PHY-LEARN-143 Laser Applications +

Discuss measurement, communication, medicine and industry at conceptual level.

144 PHY-LEARN-144 Optics Derivation Strategy +

Begin from geometry/path difference or field superposition and state approximations explicitly.

145 PHY-LEARN-145 Temperature and Thermal Equilibrium +

Understand temperature through equilibrium and the zeroth-law concept.

146 PHY-LEARN-146 Perfect Gas +

Apply ideal-gas equation and microscopic assumptions.

147 PHY-LEARN-147 Real Gases +

Understand deviations from ideal behavior.

148 PHY-LEARN-148 Van der Waals Equation +

Interpret excluded volume and intermolecular-attraction corrections.

149 PHY-LEARN-149 Thermodynamic State Variables +

Distinguish state functions from path-dependent heat and work.

150 PHY-LEARN-150 Internal Energy +

Understand microscopic energy content as a state function.

151 PHY-LEARN-151 Work in Thermodynamics +

Calculate pressure-volume work with sign convention stated.

152 PHY-LEARN-152 Heat Capacity +

Distinguish heat capacities at constant volume and pressure.

153 PHY-LEARN-153 First Law of Thermodynamics +

Apply energy conservation to thermodynamic processes.

154 PHY-LEARN-154 Isothermal Process +

Analyze ideal-gas changes at constant temperature.

155 PHY-LEARN-155 Adiabatic Process +

Derive/apply ideal-gas adiabatic relations.

156 PHY-LEARN-156 Isochoric and Isobaric Processes +

Analyze constant-volume and constant-pressure paths.

157 PHY-LEARN-157 Second Law of Thermodynamics +

Understand directionality, heat engines and entropy.

158 PHY-LEARN-158 Carnot Cycle +

Analyze the reversible benchmark heat-engine cycle.

159 PHY-LEARN-159 Carnot Efficiency +

Relate maximum reversible efficiency to reservoir temperatures.

160 PHY-LEARN-160 Refrigerators and Heat Pumps +

Define coefficients of performance and energy flows.

161 PHY-LEARN-161 Entropy +

Define entropy change for reversible paths and use it as a state function.

162 PHY-LEARN-162 Entropy and Irreversibility +

Understand entropy production in irreversible processes.

163 PHY-LEARN-163 Third Law of Thermodynamics +

Understand limiting entropy behavior near absolute zero.

164 PHY-LEARN-164 Thermodynamic Potentials +

Introduce Helmholtz/Gibbs-type potentials as useful equilibrium functions where appropriate.

165 PHY-LEARN-165 Kinetic Theory of Gases +

Connect pressure and temperature to molecular motion.

166 PHY-LEARN-166 Equipartition Principle +

Relate quadratic degrees of freedom to average energy in the classical regime.

167 PHY-LEARN-167 Maxwell Speed Distribution +

Understand distribution shape and characteristic molecular speeds.

168 PHY-LEARN-168 Mean Free Path +

Relate collision spacing to gas density and molecular scale.

169 PHY-LEARN-169 Brownian Motion +

Understand random motion as evidence of microscopic thermal agitation.

170 PHY-LEARN-170 Transport Phenomena +

Connect molecular motion to diffusion, viscosity and thermal conduction.

171 PHY-LEARN-171 Maxwell-Boltzmann Statistics +

Apply classical particle statistics in the appropriate dilute/high-temperature regime.

172 PHY-LEARN-172 Bose-Einstein Statistics +

Understand statistics of indistinguishable integer-spin particles.

173 PHY-LEARN-173 Fermi-Dirac Statistics +

Understand statistics of indistinguishable half-integer-spin particles and exclusion.

174 PHY-LEARN-174 MB-BE-FD Comparison +

Compare assumptions, occupancy restrictions and classical limits.

175 PHY-LEARN-175 Thermodynamics Problem Strategy +

Define system, process, sign convention, equation of state and applicable law before calculation.

176 PHY-LEARN-176 Coulomb's Law +

Calculate electrostatic force between point charges and use vector superposition.

177 PHY-LEARN-177 Electric Field +

Define force per unit positive test charge and calculate fields from charge distributions.

178 PHY-LEARN-178 Electric Flux +

Interpret flux through a surface.

179 PHY-LEARN-179 Gauss' Law +

Relate electric flux through a closed surface to enclosed charge.

180 PHY-LEARN-180 Gauss' Law Applications +

Exploit spherical, cylindrical or planar symmetry to calculate fields.

181 PHY-LEARN-181 Electric Potential +

Define potential difference as work per unit charge and relate potential to field.

182 PHY-LEARN-182 Potential of Point and Distributed Charges +

Calculate scalar potential by superposition/integration.

183 PHY-LEARN-183 Poisson's Equation +

Relate potential curvature to charge density.

184 PHY-LEARN-184 Laplace's Equation +

Understand source-free potential equation and boundary-value significance.

185 PHY-LEARN-185 Electrostatic Boundary Conditions +

Apply continuity/discontinuity conditions conceptually at interfaces.

186 PHY-LEARN-186 Capacitance +

Define charge storage per potential difference.

187 PHY-LEARN-187 Parallel-Plate Capacitor +

Derive capacitance with and without dielectric.

188 PHY-LEARN-188 Capacitors in Series and Parallel +

Find equivalent capacitance and charge/voltage distributions.

189 PHY-LEARN-189 Energy Stored in Electric Fields +

Relate capacitor energy to field-energy density.

190 PHY-LEARN-190 Dielectrics +

Understand polarization and field response of insulating matter.

191 PHY-LEARN-191 Polarization Vector +

Relate dipole moment density to bound charge conceptually.

192 PHY-LEARN-192 Electric Displacement +

Use D-field relationships where free and bound charges are distinguished.

193 PHY-LEARN-193 Current and Current Density +

Relate charge flow to microscopic and macroscopic current.

194 PHY-LEARN-194 Magnetic Force on Moving Charge +

Apply Lorentz magnetic force and recognize its perpendicular nature.

195 PHY-LEARN-195 Motion of Charged Particle in Magnetic Field +

Analyze circular/helical motion and cyclotron frequency conceptually.

196 PHY-LEARN-196 Force on Current-Carrying Conductor +

Relate current elements to magnetic force.

197 PHY-LEARN-197 Magnetic Field of Moving Charges +

Understand field generation by moving charge/current.

198 PHY-LEARN-198 Biot-Savart Law +

Calculate magnetic fields of simple current distributions.

199 PHY-LEARN-199 Ampere's Law +

Use circulation and symmetry to calculate magnetic fields.

200 PHY-LEARN-200 Magnetic Dipole +

Understand current-loop dipole moment, torque and energy.

201 PHY-LEARN-201 Magnetic Properties of Matter +

Distinguish diamagnetic, paramagnetic and ferromagnetic response at syllabus level.

202 PHY-LEARN-202 Magnetization and Magnetic Field H +

Relate material response quantities conceptually.

203 PHY-LEARN-203 Faraday's Law +

Relate changing magnetic flux to induced emf.

204 PHY-LEARN-204 Lenz's Law +

Determine direction of induced effects from energy-conservation reasoning.

205 PHY-LEARN-205 Self-Inductance +

Relate flux linkage to current and induced emf.

206 PHY-LEARN-206 Mutual Inductance +

Understand coupling between circuits.

207 PHY-LEARN-207 Energy Stored in Magnetic Field +

Relate inductive energy to current and field.

208 PHY-LEARN-208 Alternating Current +

Use sinusoidal voltage/current and RMS quantities.

209 PHY-LEARN-209 Pure R, L and C AC Response +

Understand amplitude and phase relationships.

210 PHY-LEARN-210 Series RLC Circuit +

Calculate impedance, phase and current.

211 PHY-LEARN-211 RLC Resonance +

Understand resonant frequency, impedance and quality factor.

212 PHY-LEARN-212 Maxwell's Equations: Integral Form +

Interpret the four field laws over finite surfaces and loops.

213 PHY-LEARN-213 Maxwell's Equations: Differential Form +

Interpret local divergence and curl equations.

214 PHY-LEARN-214 Displacement Current +

Understand Maxwell's correction and continuity of electromagnetic theory.

215 PHY-LEARN-215 Electromagnetic Waves from Maxwell Equations +

Derive propagation in vacuum and relation between E, B and wave speed.

216 PHY-LEARN-216 Poynting Vector +

Interpret electromagnetic energy flux.

217 PHY-LEARN-217 Poynting Theorem +

Understand local conservation of electromagnetic energy.

218 PHY-LEARN-218 Scalar Potential +

Use potential representation for electric fields in appropriate regimes.

219 PHY-LEARN-219 Vector Potential +

Represent magnetic field as curl of vector potential.

220 PHY-LEARN-220 Gauge Freedom +

Understand non-uniqueness of electromagnetic potentials at conceptual level.

221 PHY-LEARN-221 Electromagnetism Derivation Strategy +

Use symmetry, integral/differential law, boundary conditions and dimensional checks systematically.

222 PHY-LEARN-222 Wave-Particle Duality +

Understand experiments that require both wave and particle descriptions.

223 PHY-LEARN-223 de Broglie Hypothesis +

Relate particle momentum to matter-wave wavelength.

224 PHY-LEARN-224 Davisson-Germer-Type Evidence +

Understand electron diffraction as evidence for matter waves.

225 PHY-LEARN-225 Quantum State +

Understand a state as the mathematical carrier of information needed for quantum predictions.

226 PHY-LEARN-226 Wave Function +

Interpret ψ and probability density with normalization.

227 PHY-LEARN-227 Operators +

Understand observables as operators acting on quantum states.

228 PHY-LEARN-228 Eigenvalues and Eigenstates +

Relate measurement outcomes to operator eigenvalue problems.

229 PHY-LEARN-229 Expectation Values +

Calculate mean predicted values from normalized states.

230 PHY-LEARN-230 Commutators +

Use operator non-commutation to diagnose incompatible observables.

231 PHY-LEARN-231 Time-Dependent Schrodinger Equation +

Understand unitary time evolution of a quantum state.

232 PHY-LEARN-232 Time-Independent Schrodinger Equation +

Solve stationary-state energy eigenvalue problems.

233 PHY-LEARN-233 Boundary Conditions in Wave Mechanics +

Apply continuity/normalizability requirements to admissible solutions.

234 PHY-LEARN-234 Particle in a One-Dimensional Box +

Derive quantized energies and normalized stationary states.

235 PHY-LEARN-235 Finite Potential Well +

Understand bound states and penetration into classically forbidden regions.

236 PHY-LEARN-236 Quantum Tunneling +

Understand nonzero transmission through finite barriers and parameter dependence.

237 PHY-LEARN-237 One-Dimensional Harmonic Oscillator +

Understand quantized oscillator energy levels and ground-state energy.

238 PHY-LEARN-238 Heisenberg Uncertainty Principle +

Relate intrinsic spreads of non-commuting observables.

239 PHY-LEARN-239 Angular Momentum in Quantum Mechanics +

Understand quantization and operator structure at syllabus level.

240 PHY-LEARN-240 Spin +

Understand intrinsic angular momentum distinct from literal classical rotation.

241 PHY-LEARN-241 Spin-1/2 in a Magnetic Field +

Analyze two-state spin behavior and magnetic interaction conceptually.

242 PHY-LEARN-242 Bohr Model +

Understand quantized atomic orbits historically and derive hydrogenic energy levels within the model.

243 PHY-LEARN-243 Quantum Numbers +

Understand principal, orbital, magnetic and spin quantum numbers.

244 PHY-LEARN-244 Pauli Exclusion Principle +

Apply exclusion to electron configurations.

245 PHY-LEARN-245 Hydrogen Spectrum +

Relate transitions among quantized levels to spectral lines.

246 PHY-LEARN-246 One- and Two-Valence-Electron Spectra +

Understand term/spectral structure at syllabus depth without overextending atomic complexity.

247 PHY-LEARN-247 Photoelectric Effect +

Apply photon energy and work-function relation.

248 PHY-LEARN-248 Compton Scattering +

Derive/apply wavelength shift as photon-electron collision evidence.

249 PHY-LEARN-249 Pair Production +

Understand conversion of photon energy into particle-antiparticle mass under conservation constraints.

250 PHY-LEARN-250 Lande g-Factor +

Understand angular-momentum coupling contribution to magnetic splitting at syllabus level.

251 PHY-LEARN-251 Zeeman Effect +

Explain splitting of spectral lines in magnetic fields.

252 PHY-LEARN-252 Raman Effect +

Understand inelastic light scattering and frequency shifts due to material excitations.

253 PHY-LEARN-253 Quantum Numerical Strategy +

Identify potential, boundary conditions, operator/eigenvalue equation, normalization and requested observable.

254 PHY-LEARN-254 Crystalline Solids +

Understand long-range periodic order and crystal structure.

255 PHY-LEARN-255 Crystal Lattice and Basis +

Distinguish abstract lattice from the physical basis attached to lattice points.

256 PHY-LEARN-256 Unit Cell +

Understand primitive and conventional cells.

257 PHY-LEARN-257 Bravais Lattices +

Understand allowed translational lattice types conceptually.

258 PHY-LEARN-258 Crystal Planes and Miller Indices +

Index lattice planes and relate indices to geometry.

259 PHY-LEARN-259 X-Ray Diffraction and Bragg Law +

Use diffraction to infer crystal spacing.

260 PHY-LEARN-260 Free-Electron Model +

Understand conduction electrons as an approximate electron gas in metals.

261 PHY-LEARN-261 Fermi Energy +

Understand highest occupied energy at zero temperature in a fermion system.

262 PHY-LEARN-262 Density of States +

Understand number of available states per energy interval.

263 PHY-LEARN-263 Periodic Potential +

Understand how lattice periodicity modifies electron states.

264 PHY-LEARN-264 Band Theory +

Explain allowed bands and forbidden gaps.

265 PHY-LEARN-265 Metals, Insulators and Semiconductors +

Classify materials using band filling and band gaps.

266 PHY-LEARN-266 Intrinsic Semiconductors +

Understand thermally generated electron-hole carriers.

267 PHY-LEARN-267 Extrinsic Semiconductors +

Understand controlled doping and majority/minority carriers.

268 PHY-LEARN-268 n-Type Semiconductor +

Understand donor doping and electron majority carriers.

269 PHY-LEARN-269 p-Type Semiconductor +

Understand acceptor doping and hole majority carriers.

270 PHY-LEARN-270 p-n Junction +

Understand depletion region and built-in potential conceptually.

271 PHY-LEARN-271 Diode Characteristics +

Analyze forward/reverse bias at device-physics level.

272 PHY-LEARN-272 Transistor Physics +

Understand carrier control and amplification/switching principles at syllabus level.

273 PHY-LEARN-273 MOSFET Physics +

Understand field-effect control of a conduction channel at syllabus level.

274 PHY-LEARN-274 Dielectric Properties of Solids +

Understand polarization mechanisms and dielectric response.

275 PHY-LEARN-275 Magnetic Properties of Solids +

Distinguish major magnetic orders and response.

276 PHY-LEARN-276 Origin of Magnetism +

Relate magnetic behavior to electronic orbital/spin moments and interactions conceptually.

277 PHY-LEARN-277 Solid-State Problem Strategy +

Use lattice geometry, carrier statistics, band diagrams and device assumptions consistently.

278 PHY-LEARN-278 Nuclear Structure +

Understand nucleus in terms of protons, neutrons, size, charge and binding.

279 PHY-LEARN-279 Nuclear Radius +

Use empirical nuclear-radius scaling and interpret density implications.

280 PHY-LEARN-280 Mass Defect +

Relate constituent masses to bound-system mass.

281 PHY-LEARN-281 Binding Energy +

Calculate binding energy from mass defect.

282 PHY-LEARN-282 Binding Energy per Nucleon +

Use the curve qualitatively to understand nuclear stability and energy release.

283 PHY-LEARN-283 Nuclear Forces +

Understand short-range, strong and approximately charge-independent nuclear interaction features at syllabus level.

284 PHY-LEARN-284 Radioactivity +

Understand spontaneous nuclear transformations statistically.

285 PHY-LEARN-285 Decay Law +

Derive exponential radioactive decay.

286 PHY-LEARN-286 Half-Life and Mean Life +

Relate decay constant to characteristic times.

287 PHY-LEARN-287 Alpha Decay +

Understand alpha emission and energy accounting.

288 PHY-LEARN-288 Beta Decay +

Understand beta-minus/beta-plus/electron-capture processes and neutrino role conceptually.

289 PHY-LEARN-289 Gamma Decay +

Understand electromagnetic de-excitation of nuclei.

290 PHY-LEARN-290 Radioactive Series and Activity +

Calculate activity and sequential-decay concepts at appropriate level.

291 PHY-LEARN-291 Radiation Detection Principles +

Understand ionization, scintillation and semiconductor detection conceptually.

292 PHY-LEARN-292 Geiger-Muller Counter +

Understand operating principle, counting and limitations.

293 PHY-LEARN-293 Scintillation Detector +

Understand light production and conversion to electrical signal.

294 PHY-LEARN-294 Semiconductor Radiation Detector +

Understand electron-hole generation and energy resolution conceptually.

295 PHY-LEARN-295 Mass Spectrometer +

Understand separation/measurement by charge-to-mass response.

296 PHY-LEARN-296 Particle Accelerators +

Understand acceleration and beam-energy principles at high level.

297 PHY-LEARN-297 Cyclotron +

Derive cyclotron-frequency relation and identify relativistic limitation.

298 PHY-LEARN-298 Linear Accelerator +

Understand staged acceleration by electric fields conceptually.

299 PHY-LEARN-299 Nuclear Fission +

Understand splitting, energy release and neutron multiplication.

300 PHY-LEARN-300 Chain Reaction +

Distinguish subcritical, critical and supercritical multiplication conceptually without operational reactor guidance.

301 PHY-LEARN-301 Nuclear Reactor Principles +

Understand controlled fission, moderation, control, cooling and shielding only at educational high level.

302 PHY-LEARN-302 Nuclear Power +

Analyze energy conversion, benefits, waste and safety conceptually.

303 PHY-LEARN-303 Nuclear Fusion +

Understand light-nucleus fusion, binding-energy basis and confinement challenge.

304 PHY-LEARN-304 Fusion Applications and Challenges +

Discuss stellar energy and controlled-fusion research without operational detail.

305 PHY-LEARN-305 Elementary Particles +

Understand leptons, quarks and force carriers as basic categories.

306 PHY-LEARN-306 Conservation Laws in Particle Physics +

Apply charge, energy-momentum and relevant quantum-number conservation at syllabus level.

307 PHY-LEARN-307 Standard Model Orientation +

Understand matter particles and fundamental interactions at an introductory level.

308 PHY-LEARN-308 Nuclear Numerical Strategy +

Track atomic/nuclear masses, units, decay constants and energy conversions carefully.

309 PHY-LEARN-309 Radiation Safety Principle +

Treat radiation topics academically; do not convert syllabus knowledge into unsafe handling or construction guidance.

310 PHY-LEARN-310 Formula Sheet Architecture +

Organize formulas by assumptions and derivation origin rather than memorizing an unstructured list.

311 PHY-LEARN-311 Derivation Protocol +

State assumptions, define symbols, proceed line by line, highlight result and test dimensions/limits.

312 PHY-LEARN-312 Numerical Protocol +

Write data in SI, equation, substitution, units, significant result and sanity check.

313 PHY-LEARN-313 Diagram Protocol +

Draw labeled axes, vectors, rays, circuits or energy levels only when they clarify the solution.

314 PHY-LEARN-314 Graph Protocol +

Label variables/units and explain slope, area, intercept or limiting behavior.

315 PHY-LEARN-315 Assumption Discipline +

State idealizations such as frictionless, small-angle, ideal gas, paraxial or steady-flow conditions where relevant.

316 PHY-LEARN-316 Boundary-Condition Discipline +

In waves, quantum mechanics and fields, identify physical boundary conditions before solving.

317 PHY-LEARN-317 Vector Sign Discipline +

Fix coordinate axes and sign convention before resolving vector equations.

318 PHY-LEARN-318 Unit Discipline +

Carry units through intermediate numerical work and use dimensional consistency as an error detector.

319 PHY-LEARN-319 Approximation Discipline +

Identify the small/large parameter and justify approximation rather than silently dropping terms.

320 PHY-LEARN-320 Limiting-Case Test +

Check whether a derived result reduces to expected behavior in a known limit.

321 PHY-LEARN-321 Order-of-Magnitude Test +

Estimate scale before accepting calculator output.

322 PHY-LEARN-322 Conceptual Question Method +

Define the law/concept, explain mechanism, use a compact equation/diagram and distinguish common misconceptions.

323 PHY-LEARN-323 Derivation Question Method +

Begin from an accepted principle, not from the result to be proved.

324 PHY-LEARN-324 Numerical Question Method +

Select the governing law before searching for a formula matching listed numbers.

325 PHY-LEARN-325 Compare-and-Contrast Method +

Compare definitions, equations, assumptions, physical meaning and domains of validity.

326 PHY-LEARN-326 Past-Paper-Led but Syllabus-Controlled Preparation +

Use official past papers to learn examiner demand while retaining complete FPSC syllabus coverage.

327 PHY-LEARN-327 Physics Error Log +

Classify mistakes as concept, algebra, calculus, vector, sign, unit, approximation, diagram, boundary condition or time.

328 PHY-LEARN-328 Timed Paper-I Practice +

Rotate mechanics/relativity, fluids, waves/optics and thermodynamics under realistic time constraints.

329 PHY-LEARN-329 Timed Paper-II Practice +

Rotate electromagnetism, quantum/modern, solid-state and nuclear physics under realistic time constraints.

330 PHY-LEARN-330 Reference-Book Method +

Use standard university physics texts for derivations and concepts; reconcile notation before making final notes.

331 PHY-LEARN-331 RAHBAR Physics Rubric +

Score conceptual correctness, mathematical reasoning, derivation, units, diagrams, physical interpretation and time management. This is not an official FPSC marking formula.

332 PHY-LEARN-332 The RAHBAR Physics Standard +

The target is not formula recall but the ability to derive, calculate, interpret and communicate physics accurately under competitive-exam conditions.

333 PHY-AN-01 How to Read Physics Past Papers +

Classify every question by paper, syllabus domain, conceptual/derivation/numerical demand, mathematical tools, diagram need and marks.

334 PHY-AN-02 Mechanics Trend Matrix +

Track kinematics, dynamics, energy, momentum, rotation, gravitation and orbital mechanics.

335 PHY-AN-03 Relativity Trend Matrix +

Track Lorentz transformations, time dilation, length contraction and relativistic energy-momentum.

336 PHY-AN-04 Fluid and Elasticity Trend Matrix +

Track hydrostatics, viscosity, Bernoulli flow, surface effects and elasticity.

337 PHY-AN-05 Waves and Oscillations Trend Matrix +

Track SHM, damping, resonance, coupled systems, wave propagation and sound.

338 PHY-AN-06 Optics Trend Matrix +

Track interference, diffraction, polarization, dispersion, interferometers and lasers.

339 PHY-AN-07 Thermodynamics Trend Matrix +

Track gas laws, thermodynamic laws, entropy, cycles, kinetic theory and statistics.

340 PHY-AN-08 Electromagnetism Trend Matrix +

Track electrostatics, magnetostatics, induction, AC circuits, Maxwell equations and EM waves.

341 PHY-AN-09 Quantum and Modern Physics Trend Matrix +

Track wave mechanics, atomic physics, photons, spin, spectra and quantum applications.

342 PHY-AN-10 Solid-State Trend Matrix +

Track crystal structure, diffraction, band theory, semiconductors and material properties.

343 PHY-AN-11 Nuclear and Particle Trend Matrix +

Track binding, decay, detectors, fission/fusion and elementary particles at exam-safe academic level.

344 PHY-AN-12 Derivation Demand Analysis +

Record starting principle, assumptions, mathematical steps, final relation and limiting checks for repeated derivations.

345 PHY-AN-13 Numerical Demand Analysis +

Record governing law, common unit conversions, typical unknowns and recurring error patterns.

346 PHY-AN-14 Diagram and Graph Demand +

Identify questions where a labeled diagram, energy-level sketch, field plot or graph materially improves the answer.

347 PHY-AN-15 Five-Year Physics Diagnostic Dashboard +

Track year, paper, topic, question type, marks, error class and performance to target revision.

348 PHY-MODEL-01 Model Solution: Newtonian Dynamics +

Draw the free-body diagram, choose axes, write vector force equations and solve with sign and unit checks.

349 PHY-MODEL-02 Model Solution: Work-Energy +

Define system and forces, identify conservative/non-conservative work and apply energy balance.

350 PHY-MODEL-03 Model Solution: Momentum and Collision +

Define system, apply momentum conservation and add kinetic-energy condition only when justified.

351 PHY-MODEL-04 Model Solution: Rotational Dynamics +

Identify axis, calculate moment of inertia, torque and angular acceleration, then check translational coupling.

352 PHY-MODEL-05 Model Solution: Gravitation and Orbit +

Use gravitational field/potential or energy and centripetal dynamics according to the requested quantity.

353 PHY-MODEL-06 Model Solution: Special Relativity +

Identify frames and proper quantity before selecting Lorentz, time, length or energy-momentum relation.

354 PHY-MODEL-07 Model Solution: Hydrostatics +

Establish pressure-depth relation and boundary pressure before evaluating force or buoyancy.

355 PHY-MODEL-08 Model Solution: Viscous Flow +

State laminar/low-Reynolds assumptions before applying Poiseuille or Stokes relations.

356 PHY-MODEL-09 Model Solution: Bernoulli Flow +

Select two streamline points and combine pressure, kinetic and gravitational energy terms with continuity.

357 PHY-MODEL-10 Model Solution: Elasticity +

Identify stress/strain type, applicable modulus and elastic-limit assumption.

358 PHY-MODEL-11 Model Solution: SHM +

Derive restoring equation, identify angular frequency and use phase-consistent displacement/velocity.

359 PHY-MODEL-12 Model Solution: Damped Oscillation +

Identify damping regime from characteristic equation and interpret physical response.

360 PHY-MODEL-13 Model Solution: Forced Oscillation +

Write driven response, identify resonance condition and explain damping effects.

361 PHY-MODEL-14 Model Solution: Coupled Oscillators +

Set coupled equations, seek normal modes and solve eigenfrequency conditions.

362 PHY-MODEL-15 Model Solution: Traveling Wave +

Fix phase convention, propagation direction, wavelength/frequency and boundary conditions.

363 PHY-MODEL-16 Model Solution: Standing Wave +

Superpose counter-propagating waves and apply boundary conditions to obtain allowed modes.

364 PHY-MODEL-17 Model Solution: Doppler Effect +

Define source/observer motion signs before applying the appropriate frequency relation.

365 PHY-MODEL-18 Model Solution: Interference +

Calculate optical/path phase difference and impose constructive/destructive conditions.

366 PHY-MODEL-19 Model Solution: Diffraction +

Identify aperture geometry, approximation and minima/maxima condition before calculating pattern features.

367 PHY-MODEL-20 Model Solution: Grating +

Use grating equation, diffraction order and resolving-power relation with angular consistency.

368 PHY-MODEL-21 Model Solution: Polarization +

Use field orientation, Malus law or Brewster relation as appropriate.

369 PHY-MODEL-22 Model Solution: Laser Question +

Explain stimulated emission, inversion, pumping and resonator before characteristics/applications.

370 PHY-MODEL-23 Model Solution: First-Law Thermodynamics +

State system/sign convention and evaluate heat, work and internal-energy change.

371 PHY-MODEL-24 Model Solution: Carnot Cycle +

Track reversible isothermal/adiabatic stages and derive efficiency from reservoir temperatures.

372 PHY-MODEL-25 Model Solution: Entropy +

Choose a reversible reference path for entropy change and distinguish entropy transfer from production.

373 PHY-MODEL-26 Model Solution: Kinetic Theory +

Connect microscopic velocity statistics to pressure, temperature and characteristic speeds.

374 PHY-MODEL-27 Model Solution: Statistical Physics +

Identify MB, BE or FD regime and state occupancy/particle assumptions.

375 PHY-MODEL-28 Model Solution: Coulomb and Electric Field +

Use vector superposition and symmetry before performing component calculation or integration.

376 PHY-MODEL-29 Model Solution: Gauss Law +

Demonstrate symmetry first, select Gaussian surface and then evaluate flux.

377 PHY-MODEL-30 Model Solution: Electric Potential +

Use scalar superposition or integration and obtain field by gradient when needed.

378 PHY-MODEL-31 Model Solution: Capacitance +

Identify geometry/dielectric, derive field/potential relation and then capacitance/energy.

379 PHY-MODEL-32 Model Solution: Biot-Savart +

Define current element geometry and integrate vector contribution with symmetry.

380 PHY-MODEL-33 Model Solution: Ampere Law +

Choose an Amperian path only when symmetry makes the field factorizable.

381 PHY-MODEL-34 Model Solution: Electromagnetic Induction +

Determine flux, differentiate consistently and use Lenz law for physical direction.

382 PHY-MODEL-35 Model Solution: RLC Circuit +

Construct impedance/phasor relations, calculate resonance and interpret phase.

383 PHY-MODEL-36 Model Solution: Maxwell Equations +

State the relevant integral/differential equations, physical meaning and boundary/symmetry assumptions.

384 PHY-MODEL-37 Model Solution: Electromagnetic Wave +

Derive wave equation, propagation speed and E-B relationship from field equations.

385 PHY-MODEL-38 Model Solution: Particle in a Box +

Apply boundary conditions, normalize eigenfunctions and derive quantized energies.

386 PHY-MODEL-39 Model Solution: Quantum Tunneling +

Define barrier regions, solve/interpret wave behavior and state parameter dependence of transmission.

387 PHY-MODEL-40 Model Solution: Uncertainty Principle +

Identify conjugate observables and distinguish intrinsic spread from measurement-instrument error.

388 PHY-MODEL-41 Model Solution: Atomic Spectrum +

Use quantized levels and photon energy to calculate transition wavelength/frequency.

389 PHY-MODEL-42 Model Solution: Photoelectric Effect +

Apply photon energy balance and distinguish threshold frequency from intensity effects.

390 PHY-MODEL-43 Model Solution: Compton Effect +

Use energy-momentum conservation and wavelength-shift relation with scattering geometry.

391 PHY-MODEL-44 Model Solution: Crystal Diffraction +

Apply Miller-index geometry/Bragg condition with consistent wavelength and angle.

392 PHY-MODEL-45 Model Solution: Semiconductor +

Use band/carrier picture, doping type and junction bias before device behavior.

393 PHY-MODEL-46 Model Solution: Radioactive Decay +

Use exponential law and convert correctly among decay constant, half-life, mean life and activity.

394 PHY-MODEL-47 Model Solution: Binding Energy +

Use consistent atomic/nuclear mass conventions and convert mass defect to energy.

395 PHY-MODEL-48 Model Solution: Nuclear Reaction Energy +

Apply conservation and Q-value accounting without operational reactor or weapon guidance.

396 PHY-MODEL-49 Model Solution: Full Derivation Answer +

State law, assumptions and symbols; derive line by line; box the result; check dimensions and limiting behavior.

397 PHY-MODEL-50 Model Solution: Full Numerical Answer +

List data, convert SI units, select governing equation, substitute, calculate, state units/significant figures and sanity-check.

398 PHY-MODEL-51 Model Solution: Conceptual Physics Answer +

State the principle, mechanism and compact mathematics, then address the likely misconception.

399 PHY-MODEL-52 Model Solution: Compare-and-Contrast Physics +

Compare definition, governing equations, assumptions, physical interpretation and domain of validity.

400 PHY-PR-01 Units and Dimensions Drill +

Test equations for dimensional consistency and convert mixed-unit data to SI.

401 PHY-PR-02 Vector Mechanics Drill +

Resolve multi-force systems and verify direction with a diagram.

402 PHY-PR-03 Free-Body Diagram Drill +

Draw forces before writing equations for inclined, connected and circular-motion systems.

403 PHY-PR-04 Energy Drill +

Solve a mechanics problem by energy and verify against force-based reasoning.

404 PHY-PR-05 Momentum Drill +

Solve collision/impulse problems with clear system boundaries.

405 PHY-PR-06 Rotation Drill +

Combine translation and rotation for a rolling body.

406 PHY-PR-07 Gravitation Drill +

Derive orbital speed, period or energy from first principles.

407 PHY-PR-08 Relativity Drill +

Identify proper time/length and calculate Lorentz-factor effects.

408 PHY-PR-09 Fluid Pressure Drill +

Solve hydrostatic and buoyancy problems with pressure reference stated.

409 PHY-PR-10 Viscosity Drill +

Solve terminal-velocity or laminar-flow problems and check regime assumptions.

410 PHY-PR-11 Bernoulli Drill +

Combine continuity and Bernoulli equations in an idealized flow.

411 PHY-PR-12 Elasticity Drill +

Calculate stress, strain and deformation using the correct modulus.

412 PHY-PR-13 SHM Drill +

Move among x(t), v(t), a(t) and energy representations.

413 PHY-PR-14 Damping Drill +

Classify damping from coefficients and sketch qualitative response.

414 PHY-PR-15 Resonance Drill +

Relate driving frequency, damping and response amplitude.

415 PHY-PR-16 Normal-Mode Drill +

Solve a two-oscillator eigenfrequency problem.

416 PHY-PR-17 Wave Equation Drill +

Verify that a proposed wave function satisfies the wave equation.

417 PHY-PR-18 Standing-Wave Drill +

Apply boundary conditions to obtain harmonics.

418 PHY-PR-19 Doppler Drill +

Solve source/observer motion cases with explicit sign convention.

419 PHY-PR-20 Interference Drill +

Calculate fringe spacing and path-difference conditions.

420 PHY-PR-21 Thin-Film Drill +

Include phase reversal and optical path correctly.

421 PHY-PR-22 Diffraction Drill +

Calculate single-slit minima and interpret pattern width.

422 PHY-PR-23 Grating Drill +

Calculate wavelength/order/resolution using the grating relation.

423 PHY-PR-24 Polarization Drill +

Apply Malus and Brewster laws with angle definitions clear.

424 PHY-PR-25 Laser Concept Drill +

Explain population inversion and stimulated emission without memorized slogans.

425 PHY-PR-26 Ideal-Gas Drill +

Move among state variables and process constraints.

426 PHY-PR-27 First-Law Drill +

Solve isothermal, isobaric, isochoric and adiabatic energy balances.

427 PHY-PR-28 Carnot Drill +

Calculate efficiency/COP and explain why the reversible value is a bound.

428 PHY-PR-29 Entropy Drill +

Calculate entropy changes and identify irreversible production qualitatively.

429 PHY-PR-30 Kinetic-Theory Drill +

Calculate RMS/mean/most-probable speeds where required.

430 PHY-PR-31 Statistics Classification Drill +

Identify whether MB, BE or FD statistics applies and justify.

431 PHY-PR-32 Electrostatic Superposition Drill +

Calculate field/potential from discrete charge arrangements.

432 PHY-PR-33 Gauss-Law Drill +

Choose a valid Gaussian surface for high-symmetry charge distributions.

433 PHY-PR-34 Potential Drill +

Obtain E from V or V from charge distribution with boundary reference.

434 PHY-PR-35 Capacitor Drill +

Solve dielectric, series/parallel and stored-energy problems.

435 PHY-PR-36 Biot-Savart Drill +

Calculate field from simple current geometries.

436 PHY-PR-37 Ampere-Law Drill +

Use symmetry for wire, solenoid or related idealized configurations.

437 PHY-PR-38 Faraday-Lenz Drill +

Calculate induced emf and determine physical direction.

438 PHY-PR-39 Inductance Drill +

Solve self/mutual inductance and stored-energy problems.

439 PHY-PR-40 AC Circuit Drill +

Calculate impedance, RMS current and phase in RLC circuits.

440 PHY-PR-41 Maxwell Equation Meaning Drill +

Match each equation to its physical source/circulation meaning.

441 PHY-PR-42 EM Wave Drill +

Derive field relation and energy flux for an ideal plane wave.

442 PHY-PR-43 Quantum Normalization Drill +

Normalize a simple wave function and calculate a probability.

443 PHY-PR-44 Operator Drill +

Apply simple operators and identify eigenfunction/eigenvalue relations.

444 PHY-PR-45 Particle-in-Box Drill +

Calculate energy levels and transition energies.

445 PHY-PR-46 Tunneling Drill +

Explain how barrier width/height and particle energy affect transmission.

446 PHY-PR-47 Uncertainty Drill +

Estimate minimum uncertainty products without treating uncertainty as experimental incompetence.

447 PHY-PR-48 Hydrogen Spectrum Drill +

Calculate photon wavelength from energy-level transition.

448 PHY-PR-49 Photoelectric Drill +

Separate work function, stopping potential, frequency and intensity effects.

449 PHY-PR-50 Compton Drill +

Calculate wavelength shift for a specified scattering angle.

450 PHY-PR-51 Spin and Zeeman Drill +

Interpret quantization/splitting at syllabus level.

451 PHY-PR-52 Crystal Geometry Drill +

Determine Miller indices or interplanar relationships.

452 PHY-PR-53 Bragg Drill +

Calculate lattice spacing from diffraction data.

453 PHY-PR-54 Band-Theory Drill +

Classify conductor, semiconductor and insulator from band diagrams.

454 PHY-PR-55 Semiconductor Drill +

Identify majority carriers and junction response under bias.

455 PHY-PR-56 Decay-Law Drill +

Convert among half-life, decay constant, activity and remaining nuclei.

456 PHY-PR-57 Binding-Energy Drill +

Calculate mass defect and binding energy per nucleon.

457 PHY-PR-58 Nuclear-Conservation Drill +

Balance charge, nucleon number and energy in academic reaction equations.

458 PHY-PR-59 Detector Concept Drill +

Compare ionization, scintillation and semiconductor detector principles.

459 PHY-PR-60 Graph Interpretation Drill +

Extract physical meaning from slope, area, resonance curve, decay curve or distribution.

460 PHY-PR-61 Derivation Reconstruction Drill +

Rebuild a derivation from its governing law without looking at the final formula.

461 PHY-PR-62 Limiting-Case Drill +

Test a result in zero, small, large or classical limits where meaningful.

462 PHY-PR-63 Order-of-Magnitude Drill +

Estimate an answer before detailed calculation and reject implausible calculator output.

463 PHY-PR-64 Error-Propagation Awareness Drill +

Recognize how measurement precision and significant figures constrain a numerical conclusion.

464 PHY-PR-65 Paper-I Mixed Numerical Set +

Attempt mechanics, waves/optics and thermodynamics numericals consecutively under time pressure.

465 PHY-PR-66 Paper-II Mixed Numerical Set +

Attempt electromagnetism, quantum/solid-state and nuclear numericals consecutively under time pressure.

466 PHY-PR-67 Official Past-Paper Simulation +

Attempt an official Paper-I or Paper-II under its original annual instructions and audit every derivation/numerical.

467 PHY-PR-68 Physics Error Log +

Classify errors as concept, algebra, calculus, vector, sign, unit, approximation, boundary condition, diagram or time.

468 PHY-PR-69 RAHBAR Physics Rubric +

Score physical reasoning, mathematics, units, derivation, numerical accuracy, diagrams and interpretation. This is not an official FPSC marking formula.

469 PHY-PR-70 Four-Week Paper-I Cycle +

Week 1 mechanics/relativity; Week 2 fluids/waves; Week 3 optics/thermodynamics; Week 4 mixed timed repair.

470 PHY-PR-71 Four-Week Paper-II Cycle +

Week 1 electrostatics/magnetism; Week 2 Maxwell/AC; Week 3 quantum/solid state; Week 4 nuclear and mixed simulation.

471 PHY-PR-72 Final Formula Audit +

Verify every memorized formula by dimensions, symbols, assumptions and at least one derivation route.

472 PHY-PR-73 Final Numerical Audit +

Rework error-prone questions without notes until units, signs and physical interpretation are automatic.