Physics XII · Previous Papers 2007–2022

Frequently Asked
5-Mark Concepts

Patterns, repetitions & priority guide compiled from 15 years of CBSE board papers.

114
Questions analysed
7
Years covered
12
Recurring concepts
4
Always-asked topics

Overview

🎯 These concepts appear in EVERY or NEARLY EVERY paper — prepare these first:

  1. Young's Double Slit Experiment — conditions, fringe width derivation, comparison with diffraction  (2007, 2011, 2014×3, 2016×3)
  2. AC Generator — working principle, EMF derivation, slip rings  (2011, 2022×3)
  3. Moving Coil Galvanometer — diagram, torque, current sensitivity  (2007, 2022×2)
  4. Astronomical Telescope + Compound Microscope — ray diagrams, magnifying power  (2009, 2014×3, 2022×3)
  5. Parallel Plate Capacitor — capacitance derivation, energy stored  (2007, 2022×3)
  6. Binding Energy per Nucleon vs Mass Number — graph + explanation  (2007, 2022×3)
⚡ Wave Optics
9 questions
  • Young's Double Slit — conditions + fringe width derivation
    2007, 2011, 2014 (all 3 sets), 2016 (all 3 sets)
  • Single slit diffraction — width of central maximum
    2007 (all 3 sets), 2011
  • Interference vs Diffraction — 3 distinguishing features
    2014 (all 3 sets), 2016 (all 3 sets)
  • Polarisation — Polaroid, Malus's law, scattering by atmosphere
    2008, 2014 (all 3 sets), 2022
  • Huygens' principle — refraction of wavefront, Snell's law verification
    2007, 2011
🔋 Current Electricity
22 questions
  • Drift velocity → resistivity derivation, relaxation time
    2014 (all 3 sets), 2016 (all 3 sets)
  • Wheatstone bridge — principle + meter bridge for specific resistance
    2022 (all 3 sets)
  • Moving coil galvanometer — diagram, torque, current sensitivity, conversion
    2007, 2022 (2 sets)
🧲 Magnetic Effects
7 questions
  • Biot-Savart law — magnetic field at centre of circular loop
    2007 (OR), 2008
  • Force between two parallel current-carrying conductors
    2014 (all 3 sets)
⚡ EMI
4 questions
  • AC Generator — principle, EMF derivation (e = NBAω sinωt), slip rings
    2011, 2022 (all 3 sets)
  • Conducting rod sliding on rails — EMF, force, power (motional EMF)
    2009, 2022 (2 sets)
  • Lenz's law + mutual inductance of coaxial solenoids
    2009
🔄 Alternating Current
4 questions
  • LCR Series Circuit — phasor diagram, impedance, phase angle, resonance
    2016 (all 3 sets)
  • Transformer — function, principle, working diagram, energy losses
    2016 (all 3 sets), 2022 (OR)
  • Inductive/Capacitive reactance — graphical variation with frequency
    2007 (Set 2)
  • Quality factor of LCR — definition, methods to double Q
    2022
🔭 Ray Optics
10 questions
  • Astronomical Telescope — ray diagram, magnification, lens selection
    2009, 2014 (all 3 sets)
  • Compound Microscope — image formation at near point, magnifying power
    2014, 2022 (3 sets)
  • Total Internal Reflection in optical fibre — critical angle, ray diagram
    2008, 2007 (Set 3), 2022 (3 sets)
  • Prism — deviation vs incidence graph, refractive index at minimum deviation
    2016 (all 3 sets)
  • Refraction at spherical surface — derive object-image relation
    2022 (OR, 3 sets)
⚡ Electrostatics
6 questions
  • Parallel plate capacitor — capacitance derivation, energy stored, dielectric effect
    2007, 2022 (all 3 sets)
  • Electric dipole — torque in uniform field, stable/unstable equilibrium
    2007 (OR), 2008 (OR)
  • Gauss's law — electric field outside uniformly charged spherical shell
    2008
  • Equipotential surfaces — electric dipole, work done moving charge
    2022 (all 3 sets)
⚛️ Atoms & Nuclei
2 questions
  • Binding energy per nucleon vs mass number — graph, fission/fusion
    2007, 2022 (all 3 sets)
  • Bohr's postulates — total energy En = −13.6/n² eV, Rydberg formula
    2014 (2 sets)
  • Radioactive decay law — half-life and disintegration constant + numerical
    2007, 2014, 2022 (all 3 sets)
💻 Semiconductors
7 questions
  • Full-wave rectifier — circuit diagram, working, input/output waveforms
    2007 (Set 1), 2022 (2 sets)
  • Zener diode as voltage regulator — circuit, working, why heavily doped
    2007 (OR), 2014 (2 sets)
  • Transistor as amplifier — common emitter circuit, phase difference
    2007 (Set 1 & 3)
  • Energy band diagrams — p-type, n-type, intrinsic with impurity level
    2007, 2022
🌟 Dual Nature
4 questions
  • Photoelectric effect — Einstein's equation, stopping potential, work function
    2008, 2022 (2 sets)
  • de Broglie wavelength — derivation for electron through potential V
    2007 (OR), 2014 (all 3 sets)
  • Davisson-Germer experiment — wave nature of electrons
    2014 (all 3 sets)

🔥 Priority Study List — Ranked by Frequency

Concepts ranked by appearances across all years. Study in this order for maximum ROI.

#Concept / Question PatternTopicFrequencyYears
1 Young's Double Slit Experiment
Derive conditions for constructive/destructive interference. Find fringe width (β = λD/d). Compare with single slit diffraction (3 differences).		 Wave Optics ★★★★★
8+ times		 2007, 2011, 2014×3, 2016×3
2 AC Generator
State working principle. Derive expression for induced EMF: e = NBAω sin(ωt). State function of slip rings.		 EMI ★★★★★
6 times		 2011, 2022×3 + OR
3 Drift Velocity → Resistivity
Define drift velocity. Derive current density (J = neVd). Hence derive ρ = m/ne²τ. Factors affecting resistivity.		 Current Electricity ★★★★★
6 times		 2014×3, 2016×3
4 LCR Series Circuit
Draw phasor diagram. Derive impedance Z = √(R²+(XL-XC)²). Find phase angle. Resonance condition (XL=XC). Power factor.		 Alternating Current ★★★★
5 times		 2016×3 + 2022
5 Telescope + Compound Microscope
Draw ray diagrams. Derive magnifying power for both. Objective/eyepiece selection criteria for telescope.		 Ray Optics ★★★★
5 times		 2009, 2014×3, 2022×3
6 Moving Coil Galvanometer
Draw labelled diagram. State principle. Derive torque τ = NIAB. Current sensitivity factors. Convert to ammeter/voltmeter — radial field reason.		 Current Electricity ★★★★
4 times		 2007 (Set 1), 2022×2
7 Parallel Plate Capacitor
Derive capacitance C = ε₀A/d. Derive energy stored U = Q²/2C = ε₀E²Ad/2. Effect of inserting dielectric. Force between plates.		 Electrostatics ★★★★
4 times		 2007, 2022×3
8 Total Internal Reflection / Optical Fibre
Derive n₂/n₁ = sin(ic). Draw ray diagram for optical fibre. Explain mechanism.		 Ray Optics ★★★★
4 times		 2008, 2007 (Set 3), 2022×3
9 Binding Energy per Nucleon Graph
Draw B.E./nucleon vs mass number curve. Explain why middle nuclei are most stable. Why fission and fusion release energy.		 Atoms & Nuclei ★★★
4 times		 2007, 2022×3
10 Transformer
Function, principle, diagram. Why output current < input (step-up). Why laminated core (eddy currents). Input power > output (losses).		 Alternating Current ★★★
4 times		 2016×3, 2022 (OR)
11 Full-Wave Rectifier
Draw circuit with 2 p-n junction diodes. Explain working for both half cycles. Draw input and output waveforms.		 Semiconductors ★★★
3 times		 2007 (Set 1), 2022×2
12 Prism — Minimum Deviation
Plot deviation (δ) vs incidence angle (i). Derive μ = sin((A+δm)/2) / sin(A/2). What is dispersion? TIR in right-angled prism.		 Ray Optics ★★★
3 times		 2016×3
13 Polarisation
Distinguish unpolarised vs linearly polarised. What is Polaroid? How it produces polarised light. Scattering of sunlight by atmosphere.		 Wave Optics ★★★
3 times		 2008, 2014×3
14 de Broglie Wavelength + Davisson-Germer
Derive λ = h/√(2meV) for electron accelerated through V. Describe Davisson-Germer experiment (demonstrates wave nature of electrons).		 Dual Nature ★★★
3+ times		 2007, 2014×3
15 Bohr's Model — Hydrogen Atom
Using Bohr's postulates, derive total energy En = –13.6/n² eV. Use Rydberg formula for Lyman (n=1) and Balmer (n=2) series.		 Atoms & Nuclei ★★
2 times		 2014×2
16 Wheatstone Bridge + Meter Bridge
State working principle of Wheatstone bridge. Circuit diagram. How meter bridge is used to find specific resistance.		 Current Electricity ★★★
3 times		 2022×3
17 Radioactive Decay Numericals
Substance reduced to 1/16 in N days — find half-life. Then find remaining mass after M days. Law: N = N₀e^(–λt), t½ = 0.693/λ.		 Atoms & Nuclei ★★★
3 times (identical!)		 2022×3

Concept Patterns — Exact Question Templates

The exact question frameworks that repeat. Memorise the pattern — numerical values change but structure stays the same.

🔁 Young's Double Slit + Diffraction Comparison
4 years 2007 · 2011 · 2014×3 · 2016×3
Part A — YDSE (always appears):
"In Young's double slit experiment, deduce the conditions for (a) constructive and (b) destructive interference at a point on the screen. Draw a graph showing variation of intensity vs position 'x'."
Part B — always paired with one of:
• "Write THREE characteristic features to distinguish interference fringes (YDSE) from diffraction pattern (single slit)" — 2014×3, 2016×3
• "Calculate the wavelength" using: slit separation, screen distance, fringe position — 2007
• "If setup immersed in water, how is fringe width affected?" — 2011
🔁 AC Generator
4 times 2011 · 2022 (all 3 sets)
Fixed Template:
"(a) Write the principle of working of an AC generator. Derive the expression for the induced EMF generated in it [e = NBAω sin(ωt)]. (b) Write the function of slip rings in an AC generator."
OR Alternative (2022):
Step-up transformer — explain why: (a) output current < input current, (b) iron core is laminated, (c) input power > output power.
🔁 Telescope + Microscope (always paired)
5 times 2009 · 2014×3 · 2022×3
Standard Template (2014):
"(a) Draw a labelled ray diagram of an astronomical telescope to show image formation of a distant object. Write the main considerations for selecting objective and eyepiece lenses for large magnifying power and high resolution.
(b) A compound microscope [given f_obj, f_eye, object distance] — find distance between objective and eyepiece."
2022 Pattern:
"With the help of a ray diagram, explain the formation of image in a compound microscope when the final image is formed at the near point. Obtain the expression for the magnifying power."
🔁 Parallel Plate Capacitor
4 times 2007 · 2022×3
Core Question:
"(a) Consider a system of two parallel metal plates of area 'A', placed at separation 'd' in air. Derive the expression for the capacitance C = ε₀A/d.
(b) Find the force experienced by one plate due to the other [F = Q²/2ε₀A].
(c) Given network connected to battery — find total charge stored."
2007 Variant:
"Derive energy stored U = Q²/2C. Show U = ε₀E²Ad/2. How does energy change when separation doubled and dielectric (K=4) inserted?"
🔁 Radioactive Decay Numerical (IDENTICAL across 2022 sets)
3 times (identical!) 2022 (all 3 sets)
Exact Question (appeared in all 3 sets of 2022):
"A radioactive substance is reduced to 1/16 of its original mass after 4 days. Find the critical mass of the substance so that 4 g of substance is left after 6 days."
How to Solve:
1/16 = (1/2)⁴ → 4 half-lives in 4 days → t½ = 1 day. After 6 days = 6 half-lives. Initial mass M → M×(1/2)⁶ = 4g → M = 256g.
🔁 Moving Coil Galvanometer
3 times 2007 · 2022×2
Standard Pattern:
"(a) Draw a labelled diagram of a moving coil galvanometer. State the principle. Deduce an expression for the torque acting on a rectangular current-carrying loop in a uniform magnetic field [τ = NIAB]. Write two factors on which current sensitivity depends.
(b) Justify necessity of radial magnetic field. Calculate resistance to convert to voltmeter measuring up to V volts."
OR (2007):
State Biot-Savart law. Derive magnetic field at centre of circular loop of radius R carrying current I. Sketch field lines.

Exam Strategy by Topic

Minimum viable preparation set for 5-mark questions — tick off each item before exam day.

ELECTROSTATICS

  • Parallel plate capacitor C = ε₀A/d
  • Energy stored U = Q²/2C (field form too)
  • Torque on electric dipole τ = pE sinθ
  • Gauss's law → spherical shell E field
  • Equipotential surfaces for dipole

CURRENT ELECTRICITY

  • Drift velocity → ρ = m/ne²τ
  • Wheatstone bridge — meter bridge
  • MCG — torque, current sensitivity, conversion
  • Internal resistance of cell

MAGNETIC EFFECTS

  • Biot-Savart → B at centre of circular loop
  • MCG diagram + working
  • Force between parallel conductors
  • Velocity selector (crossed fields)

EMI

  • AC Generator — e = NBAω sin(ωt)
  • Slip rings function
  • Motional EMF — rod on rails (e = Blv)
  • Lenz's law + conservation of energy
  • Mutual inductance of coaxial solenoids

ALTERNATING CURRENT

  • LCR phasor diagram → Z, phase angle
  • Resonance condition XL = XC
  • Power factor, quality factor Q
  • Transformer — principle, energy losses
  • Inductive reactance XL = ωL vs frequency

RAY OPTICS

  • Compound microscope — ray diagram + M
  • Astronomical telescope — ray diagram + M
  • TIR → optical fibre (critical angle proof)
  • Prism: δ vs i graph, μ at min deviation
  • Mirror formula + Lens maker's equation

WAVE OPTICS

  • YDSE — fringe width β = λD/d
  • Conditions for constructive/destructive
  • Intensity vs position graph
  • Single slit — central maximum width
  • 3 differences: interference vs diffraction
  • Polarisation — Polaroid, atmospheric scattering

DUAL NATURE

  • Photoelectric effect — stopping potential
  • Einstein's equation: KEmax = hν – φ
  • de Broglie: λ = h/√(2meV)
  • Davisson-Germer experiment
  • de Broglie for different particles (compare)

ATOMS & NUCLEI

  • Bohr model → En = –13.6/n² eV
  • Rydberg formula — Lyman, Balmer series
  • B.E./nucleon vs mass number graph
  • Fission/fusion energy release explanation
  • Radioactive decay: t½ = 0.693/λ (+ numericals)

SEMICONDUCTORS

  • Full-wave rectifier — circuit + waveforms
  • Zener diode as voltage regulator
  • Transistor as amplifier (common emitter)
  • Energy band diagrams (p-type, n-type)
  • p-n junction forward/reverse bias + I-V

Q&A — Model Answers with Mark Split

For each concept: 4–5 ways the question is asked, then a model answer showing exactly how to earn each mark.

Young's Double Slit Experiment (YDSE)
8+ times
5 ways they can ask:
  1. "In YDSE, deduce conditions for (a) constructive and (b) destructive interference. Draw graph of intensity vs position 'x'."
  2. "Using Huygens' principle, explain interference of light. Derive expression for fringe width β = λD/d."
  3. "What is meant by coherent sources? State conditions for sustained interference. Find fringe width when slits are 0.5 mm apart, screen 1 m away, λ = 600 nm."
  4. "Write THREE characteristic features distinguishing interference fringes (YDSE) from single-slit diffraction."
  5. "In YDSE, if the apparatus is immersed in water (n = 4/3), how is fringe width affected? What happens if one slit is closed?"
📝 Show Model Answer (5 marks)
1 mark
Diagram: Two slits S₁ and S₂ separated by d, screen at distance D. Path difference at point P at height y: Δ = yd/D
S S₁ S₂ Screen P y d D bright
2 marks
Conditions for interference:
  • Constructive (bright fringe): Δ = nλ → yn = nλD/d (n = 0, ±1, ±2...)
  • Destructive (dark fringe): Δ = (2n−1)λ/2 → yn = (2n−1)λD/2d
1 mark
Fringe width: Distance between consecutive bright (or dark) fringes: β = λD/d. β increases if λ↑, D↑ or d↓. In water: βwater = β/n (decreases).
1 mark
Intensity graph: I = 4I₀cos²(δ/2) where δ = 2πΔ/λ. Graph: uniform equally spaced peaks, minima = 0. YDSE vs single slit: (i) equal intensity fringes vs unequal, (ii) equal width vs central is double, (iii) bright/dark alternate vs intensity pattern varies.
✅ Mark split: Diagram 1 + Conditions 2 + Fringe width 1 + Graph/distinction 1= 5 marks
AC Generator
6 times
5 ways they can ask:
  1. "Write the principle of working of an AC generator. Derive the expression for induced EMF [e = NBAω sin(ωt)]."
  2. "Draw a labelled diagram of an AC generator. Write the function of slip rings."
  3. "An AC generator has coil of N = 100 turns, area A = 0.5 m², B = 0.2 T, ω = 100π rad/s. Find peak EMF and its value at t = 1/600 s."
  4. "Why is the EMF produced by an AC generator sinusoidal? What determines its frequency?"
  5. "How is an AC generator different from a DC generator? What modification converts one to the other?"
📝 Show Model Answer (5 marks)
1 mark
Principle: Based on electromagnetic induction (Faraday's law). When a coil rotates in a uniform magnetic field, the magnetic flux through it changes periodically → an alternating EMF is induced.
1 mark
Labelled diagram: Rectangular coil ABCD (N turns) between poles of magnet, rotating about axis perpendicular to B. Two slip rings connected to brushes for external circuit.
N S A B D C slip rings brushes R → → B
2 marks
Derivation of EMF:
Magnetic flux at angle θ = ωt: Φ = NBA cos(ωt)
By Faraday's law: e = −dΦ/dt = NBAω sin(ωt)
e = e₀ sin(ωt), where peak EMF e₀ = NBAω
Frequency of AC: f = ω/2π = (number of rotations per second).
1 mark
Function of slip rings: Maintain continuous electrical contact between the rotating coil and the stationary external circuit. They allow the coil to rotate freely while delivering alternating current. (DC generator uses split-ring commutator instead, which reverses connections every half cycle.)
✅ Mark split: Principle 1 + Diagram 1 + EMF derivation 2 + Slip rings 1= 5 marks
Drift Velocity → Resistivity Derivation
6 times
5 ways they can ask:
  1. "Define drift velocity. On the basis of electron drift, derive expression for resistivity ρ = m/ne²τ."
  2. "Derive the relation between current density J and drift velocity vd. Hence derive Ohm's law."
  3. "What is relaxation time? How does resistivity depend on temperature? Explain with graph."
  4. "Two conductors A and B have resistivities ρ_A and ρ_B. What does it mean? Which material would you choose for heating element, and why?"
  5. "Derive: J = σE, where σ is the electrical conductivity. What does σ depend on?"
📝 Show Model Answer (5 marks)
1 mark
Drift velocity: Average velocity acquired by free electrons in a conductor under an applied electric field E, in the direction opposite to E. Under field E, each electron accelerates: a = eE/m. Average velocity between collisions (relaxation time τ): vd = eEτ/m
1 mark
Current derivation: In time dt, electrons in volume (A·vd·dt) cross a cross-section. Number of electrons = n·A·vd·dt. Charge = neAvd·dt.
I = neAvd
2 marks
Resistivity derivation:
Current density: J = I/A = nevd = ne·(eEτ/m) = ne²τE/m
Comparing with J = σE (Ohm's law in vector form):
Conductivity: σ = ne²τ/m
Resistivity: ρ = 1/σ = m/ne²τ
1 mark
Factors affecting ρ: (i) Temperature: as T↑, lattice vibrations increase, τ decreases → ρ increases (for metals). (ii) Impurities: impurity atoms scatter electrons, reduce τ → ρ increases. (iii) n: more free electrons → lower ρ (why metals have low ρ).
✅ Mark split: Drift velocity 1 + Current 1 + Resistivity derivation 2 + Factors 1= 5 marks
LCR Series Circuit
5 times
5 ways they can ask:
  1. "Draw phasor diagram for series LCR circuit. Derive impedance Z = √(R² + (XL−XC)²) and phase angle φ."
  2. "What is resonance in LCR circuit? Derive expression for resonant frequency ω₀ = 1/√LC."
  3. "In a series LCR circuit, R = 10 Ω, L = 0.1 H, C = 100 μF, f = 50 Hz. Find Z, phase angle and power factor."
  4. "Define quality factor Q of LCR circuit. How can you (a) double Q without changing resonant frequency? (b) What is significance of high Q?"
  5. "Explain why a series LCR circuit at resonance behaves as a purely resistive circuit. What is its power factor?"
📝 Show Model Answer (5 marks)
1 mark
Phasor diagram: VR along x-axis (in phase with I). VL leads I by 90° (upward). VC lags I by 90° (downward). Net voltage V = √(VR² + (VL−VC)²). Phase angle φ between V and I.
VR VL VC VL−VC V φ ← I
2 marks
Impedance derivation:
V² = VR² + (VL − VC)² = (IR)² + (IXL − IXC)²
(V/I)² = R² + (XL − XC)²
Z = √(R² + (XL − XC)²)
tan φ = (XL − XC)/R
where XL = ωL, XC = 1/ωC.
1 mark
Resonance: When XL = XC → ωL = 1/ωC → ω₀ = 1/√LC. At resonance: Z = R (minimum), I = V/R (maximum), φ = 0 (purely resistive), power factor cos φ = 1.
1 mark
Quality factor: Q = ω₀L/R = 1/(ω₀CR). High Q → sharp resonance, narrow bandwidth. To double Q: halve R (keeping L, C same). Or use a coil with twice the inductance and half R.
✅ Mark split: Phasor 1 + Z derivation 2 + Resonance 1 + Q factor 1= 5 marks
Astronomical Telescope
5 times
4 ways they can ask:
  1. "Draw a labelled ray diagram of astronomical telescope showing image formation of a distant object at infinity. Derive magnifying power."
  2. "Write the main considerations for selecting the objective and eyepiece lenses of a telescope for (a) large magnifying power (b) high resolving power."
  3. "An astronomical telescope has objective of focal length 200 cm and eyepiece of 5 cm. Find: (a) magnifying power for normal adjustment (b) length of telescope."
  4. "What is the difference between a refracting and reflecting telescope? Why are large astronomical telescopes always reflecting type?"
📝 Show Model Answer (5 marks)
1 mark
Ray diagram (normal adjustment): Parallel rays from distant object refracted by objective → real image at F₀ (common focal point). Eyepiece (focal length fe) → final image at infinity.
Objective (fo large) Eyepiece (fe small) Fo=Fe I' (inverted) fo final image at ∞
2 marks
Magnifying power derivation:
m = angle subtended by final image (β) / angle subtended by object (α)
α = h/f₀ (angle of object at objective), β = h/fe (angle of image at eyepiece)
m = f₀/fe (normal adjustment — final image at ∞)
For image at near point D: m = f₀(1/fe + 1/D)
Length of telescope (normal adjustment): L = f₀ + fe
1 mark
Lens selection:
  • For large magnification: large f₀, small fe
  • For high resolution: large aperture objective (resolving power ∝ aperture D)
  • Eyepiece: comfortable eye-relief; can be simple plano-convex or Ramsden
1 mark
Reflecting vs Refracting: Reflecting telescopes use concave mirror (no chromatic aberration, cheaper to make large, mirror can be supported from back). Large telescopes are always reflecting because large lenses sag under gravity; mirrors don't have chromatic aberration.
✅ Mark split: Diagram 1 + m derivation 2 + Lens selection 1 + Reflecting vs refracting 1= 5 marks
Compound Microscope
5 times
4 ways they can ask:
  1. "With the help of a ray diagram, explain image formation in a compound microscope when final image is formed at the near point. Derive magnifying power."
  2. "A compound microscope has objective of focal length 1 cm, eyepiece of 5 cm. Object is at 1.1 cm from objective. Find distance between the lenses for image at 25 cm."
  3. "How does magnifying power of compound microscope change when: (a) focal length of eyepiece is decreased, (b) tube length is increased?"
  4. "Distinguish between simple microscope and compound microscope with diagrams. When is a compound microscope preferred?"
📝 Show Model Answer (5 marks)
1 mark
Ray diagram: Object AB just beyond F₀ of objective → real, magnified, inverted image A'B' formed beyond 2F₀. A'B' acts as virtual object for eyepiece → eyepiece forms final virtual image A''B'' at near point D (25 cm). Final image: inverted, highly magnified.
2 marks
Magnifying power derivation:
M = m₀ × me (product of individual magnifications)
Magnification by objective: m₀ = L/f₀ (where L = image distance from objective ≈ tube length)
Magnification by eyepiece: me = (1 + D/fe) (image at near point D)
Total: M = (L/f₀)(1 + D/fe)
For high M: f₀ small, fe small, L large.
1 mark
Length calculation: Total length = distance between objective and eyepiece = image distance from objective (v₀) + fe (for relaxed eye) or v₀ + u_e (where u_e = object distance for eyepiece when image at D).
1 mark
When used: When magnification required is much greater than a simple microscope can provide. Simple microscope: M = 1 + D/f (max ~10). Compound microscope: M can be several hundred.
✅ Mark split: Diagram 1 + M derivation 2 + Length 1 + Comparison 1= 5 marks
Moving Coil Galvanometer (MCG)
4 times
5 ways they can ask:
  1. "Draw a labelled diagram of a moving coil galvanometer. State its principle. Derive expression for torque τ = NIAB."
  2. "Write two factors on which current sensitivity depends. How is a galvanometer converted to: (a) ammeter (b) voltmeter?"
  3. "Why is a radial magnetic field used in a MCG? What is the significance of a soft iron core?"
  4. "A galvanometer has G = 30 Ω, Ig = 2 mA. Find shunt to convert to ammeter of range 0–2 A. Find series resistance to convert to voltmeter of range 0–5 V."
  5. "Compare current sensitivity and voltage sensitivity of a galvanometer. Is a more current-sensitive galvanometer always more voltage-sensitive? Justify."
📝 Show Model Answer (5 marks)
1 mark
Labelled diagram: Rectangular coil (N turns) between curved pole pieces of a permanent magnet. Soft iron core inside coil ensures radial field. Spring provides restoring torque.
N S soft iron core coil suspension scale spring → →
2 marks
Principle and torque:
A current-carrying coil in magnetic field experiences a deflecting torque.
τ_deflecting = F × b = (BIl) × b = BIA (for one turn)
For N turns: τ = NIAB
At equilibrium: NIAB = kθ (k = torsional constant of spring)
θ = (NBA/k)·I → deflection proportional to current.
Radial field: ensures sinθ = 1 always → uniform scale.
1 mark
Current sensitivity = θ/I = NBA/k. Increase by: (i) increasing N, B, A or (ii) decreasing k (use finer suspension wire).
Conversion to ammeter: Connect low resistance shunt S in parallel: S = IgG/(I − Ig)
Conversion to voltmeter: Connect high resistance R in series: R = V/Ig − G
1 mark
Numerical: Shunt: S = (2×10⁻³ × 30)/(2 − 2×10⁻³) ≈ 0.03 Ω. Series resistance: R = 5/(2×10⁻³) − 30 = 2470 Ω.
✅ Mark split: Diagram 1 + Principle/torque 2 + Sensitivity/conversion 1 + Numerical 1= 5 marks
Parallel Plate Capacitor
4 times
5 ways they can ask:
  1. "Derive the expression for capacitance of a parallel plate capacitor C = ε₀A/d. How is it affected by a dielectric?"
  2. "Derive expression for energy stored in a capacitor: U = Q²/2C. Show that U = ε₀E²Ad/2. Explain energy density."
  3. "What happens to capacitance, charge, voltage, and energy when: (a) battery remains connected and dielectric inserted (b) battery disconnected then dielectric inserted?"
  4. "Find the force between the plates of a charged capacitor. Derive F = Q²/2ε₀A."
  5. "Three capacitors 2 μF, 3 μF, 6 μF are connected to 12 V battery. Find total energy stored in: (a) series connection (b) parallel connection."
📝 Show Model Answer (5 marks)
1 mark
Setup/diagram: Two parallel conducting plates area A, separation d. Plate 1: +Q, Plate 2: −Q. Uniform E field between plates.
+ − + + + + + − − − − − E d A C = ε₀A/d
2 marks
Capacitance derivation:
By Gauss's law: E = σ/ε₀ = Q/ε₀A
Potential difference: V = Ed = Qd/ε₀A
Capacitance: C = Q/V = ε₀A/d
With dielectric (κ): C = κε₀A/d — capacitance increases by factor κ.
1 mark
Energy stored:
dW = V·dq = (q/C)dq. Total: U = Q²/2C = CV²/2 = QV/2
In terms of field: U = (ε₀E²/2)·(A·d) = ε₀E²Ad/2
Energy density (energy per unit volume) = ε₀E²/2
1 mark
Effect of dielectric:
  • Battery connected: V constant, C increases (κ times), Q increases, E same, U increases (κU)
  • Battery disconnected: Q constant, C increases (κ times), V decreases (V/κ), E decreases, U decreases (U/κ)
✅ Mark split: Setup 1 + Capacitance derivation 2 + Energy 1 + Dielectric effect 1= 5 marks
Total Internal Reflection & Optical Fibre
4 times
5 ways they can ask:
  1. "State the conditions for total internal reflection. Define critical angle. Derive the relation μ = 1/sin(ic)."
  2. "Explain with a ray diagram how light is transmitted through an optical fibre using TIR. State two applications."
  3. "A glass slab has refractive index 1.732. Find critical angle. What happens when angle of incidence exceeds this value?"
  4. "Why is the core of an optical fibre made of glass with higher refractive index than the cladding? Draw a labelled diagram."
  5. "Prove that the refractive index μ = sin((A + δm)/2) / sin(A/2) for a prism at minimum deviation. How is this used to find μ?"
📝 Show Model Answer (5 marks)
1 mark
Critical angle definition: The angle of incidence in the denser medium for which the angle of refraction in the rarer medium is 90°. Below ic: refraction + partial reflection. Above ic: complete (total) internal reflection.
Rarer (air) Denser (glass) i < ic i i = ic r=90° ic i > ic (TIR) TIR!
2 marks
Derivation of critical angle:
At critical angle ic, refracted ray grazes surface (r = 90°). Apply Snell's law:
n₁ sin(ic) = n₂ sin(90°) = n₂
sin(ic) = n₂/n₁
For glass–air interface: sin(ic) = 1/μ → μ = 1/sin(ic)
Example: μ = 1.5 → ic = sin⁻¹(1/1.5) = 41.8°
1 mark
Optical fibre (diagram + working): Core (dense glass, n₁) surrounded by cladding (less dense glass/plastic, n₂ < n₁). Light enters at one end and hits core-cladding interface at angle > ic → TIR → light travels along fibre by successive TIR even around bends.
1 mark
Conditions for TIR: (i) Light must travel from denser to rarer medium. (ii) Angle of incidence > critical angle.
Applications: (i) Telecommunication — carry digital signals as light pulses over long distances with minimal loss. (ii) Medical endoscopy — transmit images from inside body.
✅ Mark split: Critical angle definition 1 + Derivation 2 + Optical fibre 1 + Conditions/applications 1= 5 marks
Binding Energy per Nucleon Graph
4 times
4 ways they can ask:
  1. "Draw the curve of binding energy per nucleon vs mass number. Label key features. Explain why iron-56 is the most stable nucleus."
  2. "Using B.E./A vs A graph, explain why (a) fission of U-235 releases energy (b) fusion of deuterium and tritium releases energy."
  3. "Define mass defect and binding energy. Calculate B.E. of ₂⁴He given: mass of He = 4.0026 u, mp = 1.0078 u, mn = 1.0087 u."
  4. "Why does the B.E./A graph decrease for heavy nuclei? How does this make them unstable compared to medium nuclei?"
📝 Show Model Answer (5 marks)
2 marks
B.E./A vs A curve (accurate features):
B.E./nucleon (MeV) Mass Number (A) 0 2 4 6 8 10 10 50 100 200 Fe-56 ~8.7 MeV (peak) U-238 H He-4 ← fission fusion→
  • Starts very low for H-1 (0), rises steeply for light nuclei (He-4: ~7.1 MeV)
  • Peak at A ≈ 56 (Fe/Ni): ~8.7 MeV/nucleon — most stable
  • Gradually decreases for heavy nuclei (U-235: ~7.6 MeV)
  • Sharp peaks for He-4, C-12, O-16 (magic numbers)
1 mark
Stability: Higher B.E./A → more energy required to break nucleus → more stable. Iron-56 at peak means maximum energy needed to remove any nucleon → most stable naturally occurring nucleus.
1 mark
Nuclear Fission: Heavy nucleus (A~235) at B.E./A ≈ 7.6 MeV splits into two medium nuclei (A~115) at B.E./A ≈ 8.4 MeV. Energy released = (8.4 − 7.6) × 235 ≈ 188 MeV per fission. Products are more stable.
1 mark
Nuclear Fusion: Light nuclei (D + T, B.E./A ~1–3 MeV) combine to form He-4 (B.E./A ~ 7.1 MeV). Gain in B.E./A is larger than fission → more energy per unit mass released. Requires extremely high temperature (~10⁷ K) to overcome Coulomb repulsion.
✅ Mark split: Graph with features 2 + Stability 1 + Fission 1 + Fusion 1= 5 marks
Radioactive Decay Law & Numericals
3 times (identical in 2022!)
4 ways they can ask:
  1. "State the law of radioactive decay. Derive N = N₀e^(−λt). Define half-life and show t½ = 0.693/λ."
  2. [EXACT 2022 question] "A radioactive substance is reduced to 1/16 of its original mass in 4 days. Find the original mass if 4 g remains after 6 days."
  3. "The half-life of ²³⁸U is 4.5 × 10⁹ years. If a rock sample contains equal amounts of U-238 and Pb-206 (daughter), estimate age of rock."
  4. "Define activity of a radioactive sample. State its SI unit. Show that activity A = λN = λN₀e^(−λt)."
📝 Show Model Answer (5 marks)
1 mark
Decay law: Rate of decay is proportional to number of undecayed nuclei N: dN/dt = −λN (λ = disintegration constant). Solution: N = N₀e^(−λt)
1 mark
Half-life derivation: At t = t½, N = N₀/2: N₀/2 = N₀e^(−λt½) → e^(λt½) = 2 → t½ = ln2/λ = 0.693/λ
1 mark
Step 1 — Find half-life: In 4 days, N = N₀/16 = N₀·(1/2)⁴. This means 4 half-lives in 4 days → t½ = 1 day
1 mark
Step 2 — Find initial mass: After 6 days = 6 half-lives: N = N₀·(1/2)⁶ = N₀/64. Given N = 4g: N₀ = 4 × 64 = 256 g
1 mark
Activity: A = |dN/dt| = λN = λN₀e^(−λt) = A₀e^(−λt). SI unit: Becquerel (Bq) = 1 disintegration per second. Also curie: 1 Ci = 3.7 × 10¹⁰ Bq.
✅ Mark split: Decay law 1 + Half-life 1 + Find t½ 1 + Find N₀ 1 + Activity 1= 5 marks
Full-Wave Rectifier
3 times
4 ways they can ask:
  1. "Draw circuit diagram of a full-wave rectifier using two p-n junction diodes. Explain its working. Draw input and output waveforms."
  2. "Why is a full-wave rectifier preferred over a half-wave rectifier? What is its ripple frequency compared to input?"
  3. "What is a centre-tap transformer? How does it help in full-wave rectification?"
  4. "How does adding a filter capacitor improve the output of a full-wave rectifier? Sketch the smoothed output."
📝 Show Model Answer (5 marks)
1 mark
Circuit diagram: Centre-tap transformer, D₁ and D₂, output across RL. Both half-cycles produce current in same direction through RL.
Trans- former A(+) M B(−) D₁ D₂ RL Output: pulsating DC
2 marks
Working:
Positive half cycle (A is +ve): D₁ forward biased, D₂ reverse biased. Current flows: A → D₁ → RL → M. Output at RL is positive.
Negative half cycle (B is +ve): D₂ forward biased, D₁ reverse biased. Current flows: B → D₂ → RL → M. Current through RL is in same direction. Output is again positive.
→ Both half cycles give current in same direction through RL.
1 mark
Waveforms:
Input: Sinusoidal AC wave (alternating +ve and −ve half cycles at frequency f).
Output: Pulsating DC — both half cycles appear as positive humps. Ripple frequency = 2f (twice the input).
1 mark
Advantage over half-wave: Efficiency ~81% vs ~41%. Both half cycles utilised → better DC output. Filter capacitor charges and discharges slowly → smoother DC. Ripple voltage is lower and easier to filter.
✅ Mark split: Circuit 1 + Working 2 + Waveforms 1 + Advantages 1= 5 marks
Polarisation of Light
3 times
4 ways they can ask:
  1. "What is meant by polarisation of light? Distinguish between unpolarised and plane-polarised light. How is polarised light produced using a Polaroid?"
  2. "State and prove Malus's law. When two polaroids are placed with their axes (a) parallel (b) perpendicular, what fraction of incident intensity is transmitted?"
  3. "Define Brewster's angle. Prove tan(θB) = μ. Why is reflected light at Brewster's angle completely polarised?"
  4. "Explain why: (a) sky is blue (b) sunset appears red. How is scattering related to polarisation?"
📝 Show Model Answer (5 marks)
1 mark
Polarisation: Light is a transverse wave — electric field E oscillates perpendicular to propagation direction. Unpolarised light: E oscillates in all planes. Plane-polarised light: E oscillates in only one plane (plane of polarisation). Light is transverse (proved by polarisation); sound cannot be polarised as it is longitudinal.
1 mark
Polaroid: Sheet of polyvinyl alcohol with elongated molecules aligned by stretching and stained with iodine. Molecules absorb E-field component along their length (pass axis = direction perpendicular to chain). Transmits only one component → linearly polarised light.
1 mark
Malus's Law: When polarised light of intensity I₀ passes through analyser at angle θ to polariser axis: I = I₀ cos²θ. At θ = 0°: I = I₀ (maximum). At θ = 90°: I = 0 (minimum/extinction). [Used to verify light is polarised].
1 mark
Brewster's law: At Brewster's angle θ_B, reflected ray ⊥ refracted ray. Using geometry: θ_B + θ_r = 90° → θ_r = 90° − θ_B. Snell's law: n = sin(θ_B)/sin(θ_r) = sin(θ_B)/cos(θ_B) = tan(θ_B). Reflected light at θ_B is completely plane polarised.
1 mark
Atmospheric scattering: Rayleigh scattering: scattered intensity ∝ 1/λ⁴. Blue light (short λ) scattered much more → sky appears blue. At sunset/sunrise, light travels longer path → most blue scattered away → sky appears red/orange.
✅ Mark split: Polarisation 1 + Polaroid 1 + Malus's law 1 + Brewster's law 1 + Scattering 1= 5 marks
Gauss's Law & Electric Field of Charged Shell
6+ times
4 ways they can ask:
  1. "State Gauss's law. Using it, derive the expression for electric field at a point (a) outside, (b) on the surface, and (c) inside a uniformly charged spherical shell."
  2. "State Gauss's law in electrostatics. Apply it to find the electric field due to an infinitely long straight uniformly charged wire."
  3. "Using Gauss's law, derive electric field due to a uniformly charged infinite plane sheet. Why is the field uniform and independent of distance?"
  4. "State Gauss's law. Obtain electric field lines for a system of two equal and opposite charges (electric dipole). Sketch the field lines."
📝 Show Model Answer (5 marks)
1 mark
Gauss's Law: The total electric flux through any closed surface is equal to 1/ε₀ times the total charge enclosed by that surface: Φ = ∮ E⃗·dA⃗ = Q_enc/ε₀
Diagram
Setup: Spherical shell of radius R, surface charge density σ, total charge Q = 4πR²σ. Gaussian surface = concentric sphere of radius r.
Charged shell (R) r > R r < R Outside: E = Q/4πε₀r² Inside: E = 0
2 marks
Derivation (outside, r > R): Gaussian sphere radius r. By symmetry, E is radial and uniform on surface. Flux: Φ = E × 4πr². Charge enclosed = Q. By Gauss's law: E × 4πr² = Q/ε₀ → E = Q/4πε₀r² = kQ/r² (like a point charge).

Inside (r < R): No charge inside shell. Q_enc = 0. ∴ E × 4πr² = 0 → E = 0 everywhere inside the shell.
1 mark
On the surface (r = R): E = Q/4πε₀R² = σ/ε₀. Conclusion: Shell acts as a point charge for points outside; perfect shielding for points inside (basis of Faraday cage).
✅ Mark split: Statement 1 + Diagram 1 + Outside derivation 1 + Inside 1 + Surface 1= 5 marks
Transformer
5+ times
4 ways they can ask:
  1. "State the principle of a transformer. With a labelled diagram, explain its working. Derive the relation between turns ratio and voltage ratio."
  2. "Explain why: (a) output current < input current in a step-up transformer, (b) iron core is laminated, (c) transformer core is made of soft iron."
  3. "Define efficiency of a transformer. What are the various energy losses in a transformer? How are they minimised?"
  4. "A step-up transformer has 100 primary turns and 1000 secondary turns. If input is 220 V at 5 A, find output voltage, output current, and input power (ideal transformer)."
📝 Show Model Answer (5 marks)
1 mark
Principle: Mutual induction — when AC flows through primary coil, changing flux links with secondary, inducing EMF by Faraday's law. Works only with AC (not DC) as DC produces no changing flux.
Diagram
Labelled diagram:
Primary N_P turns Secondary N_S turns AC in V_P, I_P AC out V_S, I_S Laminated soft iron core Φ →
2 marks
Derivation: EMF induced in primary (back-EMF): V_P = N_P × dΦ/dt. EMF in secondary: V_S = N_S × dΦ/dt. Dividing: V_S/V_P = N_S/N_P = k (turns ratio). For ideal transformer (no losses): Input power = Output power → V_P·I_P = V_S·I_S → I_S/I_P = N_P/N_S = 1/k. Step-up: k > 1, voltage rises, current falls.
1 mark
Energy losses & remedies: (i) Copper loss (I²R in windings) → use thick low-resistance wire. (ii) Iron/Eddy current loss → laminate core (thin insulated sheets). (iii) Hysteresis loss → use soft iron (low retentivity) as core. (iv) Flux leakage → wind secondary over primary. Efficiency η = P_out/P_in × 100%.
✅ Mark split: Principle 1 + Diagram 1 + Derivation 2 + Losses 1= 5 marks
Refraction at Spherical Surface & Lens Maker's Equation
4+ times
4 ways they can ask:
  1. "Derive the lens maker's formula: 1/f = (n-1)[1/R₁ - 1/R₂]. State the assumptions made."
  2. "Derive the relation for refraction at a single spherical surface: n₂/v - n₁/u = (n₂-n₁)/R."
  3. "Define power of a lens. Derive the expression for equivalent focal length of two thin lenses in contact: 1/f = 1/f₁ + 1/f₂."
  4. "A convex lens of focal length 20 cm is placed in contact with a concave lens of focal length 30 cm. Find the power and nature of the combination."
📝 Show Model Answer (5 marks)
1 mark
Refraction at surface 1 (object in medium n₁): Using the formula for a single spherical surface with centre of curvature C₁, radius R₁: n₂/v₁ - n₁/u = (n₂ - n₁)/R₁ where v₁ is the image formed by surface 1 (acts as virtual object for surface 2).
Diagram
Thin convex lens geometry:
C₁ C₂ O I u v R₁ R₂
2 marks
Refraction at surface 2 (image I₁ acts as object): n₁/v - n₂/v₁ = (n₁ - n₂)/R₂

Adding both equations (v₁ terms cancel for thin lens):
n₁/v - n₁/u = (n₂ - n₁)[1/R₁ - 1/R₂]
Dividing by n₁: 1/v - 1/u = (n₂/n₁ - 1)[1/R₁ - 1/R₂]
By lens formula, 1/v - 1/u = 1/f, so:
1/f = (n - 1)[1/R₁ - 1/R₂] where n = n₂/n₁ (refractive index of lens w.r.t. medium).
1 mark
Two lenses in contact: Image by lens 1: 1/v₁ - 1/u = 1/f₁. Lens 2 uses v₁ as object: 1/v - 1/v₁ = 1/f₂. Adding: 1/v - 1/u = 1/f₁ + 1/f₂ → 1/f = 1/f₁ + 1/f₂. Power: P = P₁ + P₂ (in dioptres, P = 1/f in metres).
✅ Mark split: Surface 1 derivation 1 + Diagram 1 + Surface 2 + Lens maker 2 + Combination 1= 5 marks
Biot-Savart Law & Ampere's Circuital Law
4+ times
4 ways they can ask:
  1. "State Biot-Savart law. Using it, derive the expression for magnetic field at the centre of a circular current-carrying loop."
  2. "State Ampere's circuital law. Use it to find the magnetic field inside and outside a long straight solenoid."
  3. "Using Biot-Savart law, find the magnetic field at a point on the axis of a circular loop. Hence compare with the field at the centre."
  4. "State Biot-Savart law and Ampere's circuital law. Which is more general? Why can Ampere's law only be used in cases of high symmetry?"
📝 Show Model Answer (5 marks)
1 mark
Biot-Savart Law: Magnetic field dB due to a small current element I·dl at distance r: dB = (μ₀/4π) · (I dl sinθ)/r². Direction: perpendicular to both dl and r (right-hand screw rule). Vector form: dB⃗ = (μ₀/4π)(I dl⃗ × r̂)/r².
Diagram
Circular loop setup:
→ I O (centre) B (out) R dl B = μ₀I/2R (at centre)
2 marks
Derivation — B at centre of circular loop: Each element dl is ⊥ to r (θ = 90°), so dB = μ₀I dl/4πR². All dB point in same direction (axially, by right-hand rule). Integrating over full loop (∮dl = 2πR):
B = μ₀I × 2πR / (4πR²) = μ₀I/2R
For N turns: B = μ₀NI/2R.
1 mark
Ampere's Law + Solenoid: ∮B⃗·dl⃗ = μ₀I_enc. For solenoid (n turns/m, length L): Rectangular Amperian loop with one side inside (length l), three sides contributing zero. B·l = μ₀·(nl)·I → B = μ₀nI. Inside: uniform field; outside: B ≈ 0.
✅ Mark split: Biot-Savart statement 1 + Diagram 1 + Circular loop derivation 2 + Ampere/solenoid 1= 5 marks
Photoelectric Effect
4+ times
4 ways they can ask:
  1. "State Einstein's photoelectric equation. Explain how it accounts for (a) threshold frequency, (b) kinetic energy dependence on frequency, (c) independence from intensity."
  2. "Draw a labelled diagram of Lenard's experimental setup for photoelectric effect. Draw and explain the I-V graph for two different frequencies of incident light."
  3. "What is stopping potential? How does it vary with (a) frequency, (b) intensity of light? How does this contradict the wave theory?"
  4. "The work function of a metal is 2 eV. Find (a) threshold frequency, (b) maximum KE of photoelectrons when light of frequency 8×10¹⁴ Hz is incident."
📝 Show Model Answer (5 marks)
1 mark
Wave theory failures: (i) No emission below threshold frequency, regardless of intensity — wave theory predicts emission at any frequency with enough intensity. (ii) Emission is instantaneous — wave theory predicts time delay to accumulate energy. (iii) Max KE depends on frequency not intensity — wave theory predicts KE ∝ intensity.
Diagram
Experimental setup + I-V graph:
Evacuated tube E C hν e⁻ → A V I -V_s ν₂ (higher ν) ν₁
2 marks
Einstein's photoelectric equation: Light consists of photons each carrying energy E = hν. When a photon hits metal surface, entire energy is absorbed by ONE electron. Part used to overcome work function (φ = hν₀); rest becomes KE:
KE_max = hν − φ = hν − hν₀ = h(ν − ν₀)
Also: eV_s = h(ν − ν₀) → stopping potential V_s ∝ ν (independent of intensity).
Saturation current ∝ number of photons ∝ intensity (not frequency).
1 mark
Threshold frequency ν₀: Minimum frequency below which emission doesn't occur, even at high intensity. At ν = ν₀: KE = 0, photon energy just equals work function. Work function: φ = hν₀. Photoelectric effect proves particle nature of light.
✅ Mark split: Wave theory failures 1 + Diagram 1 + Einstein's equation 2 + Threshold 1= 5 marks
Bohr's Model of Hydrogen Atom
4+ times
4 ways they can ask:
  1. "State Bohr's postulates. Derive the expression for the radius of nth orbit and total energy of the electron in nth orbit."
  2. "Using Bohr's postulates, derive the expression for the frequency/wavelength of radiation emitted when electron transitions from n₂ to n₁ level."
  3. "Explain the origin of hydrogen spectrum. Why are the spectral lines not equally spaced? What is the significance of negative energy?"
  4. "The radius of first Bohr orbit is 0.529 Å. Find radius of third orbit. If energy in first orbit is −13.6 eV, find energy in second orbit."
📝 Show Model Answer (5 marks)
1 mark
Bohr's postulates: (i) Electron revolves in certain discrete circular orbits (stationary states) without radiating energy. (ii) Angular momentum is quantised: L = mvr = nh/2π (n = 1, 2, 3...). (iii) Radiation emitted/absorbed when electron jumps between orbits: hν = E₂ − E₁.
2 marks
Derivation — radius of nth orbit: Centripetal force = Coulomb force: mv²/r = ke²/r² → mv² = ke²/r …(1). Quantisation: mvr = nh/2π → v = nh/2πmr …(2). Substituting (2) in (1): m(nh/2πmr)² = ke²/r → solving: r_n = n²h²/4π²mke² = n² × 0.529 Å.

Energy of nth orbit: KE = ½mv² = ke²/2r. PE = −ke²/r. Total E = KE + PE = −ke²/2r. Substituting r_n: E_n = −13.6/n² eV. Negative energy means bound state.
Diagram
Energy level diagram:
n=1 −13.6 eV n=2 −3.4 eV n=3 −1.51 eV n=4 −0.85 eV n=∞ 0 eV Lyman Balmer Paschen
1 mark
Frequency of emitted radiation: When electron jumps from n₂ → n₁ (n₂ > n₁): hν = E_n₂ − E_n₁ = 13.6(1/n₁² − 1/n₂²) eV. In wave number: 1/λ = R_H(1/n₁² − 1/n₂²) where R_H = 1.097 × 10⁷ m⁻¹ (Rydberg constant).
✅ Mark split: Postulates 1 + Radius + Energy derivation 2 + Diagram 1 + Frequency 1= 5 marks