Bohr model

“A hydrogen discharge tube glows red (Hα) when electrons fall from n=3 to n=2, exactly as Bohr’s Eₙ = –13.6/n² predicts.”

Bohr postulated that an electron in hydrogen occupies only quantized orbits with energies Eₙ = –13.6 eV / n² (n=1,2,…). A transition between levels emits or absorbs a photon of energy ΔE = hν. The formula applies only to hydrogen-like (single-electron) atoms; using it for multi-electron atoms is a trap.

Eₙ = −13.6/n² eV

Memory trick: E_n negative; larger n → less negative, closer to zero.

Changing fields sustain an electromagnetic wave

“When a lightning strike flashes, the sudden electric surge creates a magnetic ripple that propagates outward as a radio wave.”

A time-varying electric field generates a magnetic field (Maxwell-Ampère) and a time-varying magnetic field generates an electric field (Faraday). This mutual induction lets the disturbance travel without charges. Trap: assuming a static field can propagate—only changing fields do.

Memory trick: Changing E → B, Changing B → E

Independent horizontal and vertical motion

“A basketball’s horizontal drift stays steady while gravity pulls it down, like a car moving on a flat road while a weight hangs.”

In projectile motion, gravity acts only vertically, so vertical velocity changes as vy = uy – gt, while horizontal velocity stays constant at vx = ux (air resistance ignored). Both motions share the same time variable, so solve x and y separately then combine. Mixing the two speeds is a frequent error.

Memory trick: One clock, two equations: x = u cosθ·t, y = u sinθ·t – ½gt².

Thermal expansion — common mistake

“A metal ring with a drilled hole expands uniformly, so the hole gets larger when the ring is heated.”

When a solid is heated, every linear dimension increases by ΔL = αLΔT; thus area expands by ≈2α and volume by ≈3α for small α. A hole in the plate expands as if filled with the same material. Assuming the hole shrinks leads to incorrect stress calculations.

Memory trick: Hole expands like metal – 2α for area, 3α for volume

Temperature and molecular kinetic energy

“A hot-air balloon rises because heating the gas raises each molecule’s average translational kinetic energy, expanding the air.”

For an ideal gas, absolute temperature T measures the average translational kinetic energy per molecule: ⟨KE⟩ = 3⁄2 k_B T. At the same T, light and heavy molecules have identical ⟨KE⟩ but their rms speed v_rms = √(3k_B T/m) differs, lighter ones moving faster. Exam trap: confusing equal kinetic energy with equal speed; heavier gases do not have lower kinetic energy, only lower speed.

Memory trick: KE ∝ T; v_rms ∝ 1/√m

Field-potential relationship

“A ball rolls downhill; the slope direction is the electric field.”

The electric field points in the direction where the electric potential decreases most rapidly. In one dimension Eₓ = -dV/dx; the minus sign carries the direction information. Forgetting the minus sign makes the field point the wrong way.

Memory trick: E downhill = -gradient V

No isolated magnetic poles

“When you break a chocolate bar, each piece still has both sweet and bitter sides; similarly cutting a magnet yields smaller north-south pairs, never a lone pole.”

When a bar magnet is cut, each fragment becomes a smaller dipole with its own north and south ends; magnetic field lines are continuous, so net flux through any closed surface remains zero. This shows that isolated magnetic monopoles do not exist. A trap is assuming a cut piece can have a single pole, leading to non-zero flux calculations.

Memory trick: Cut magnet → two dipoles, no monopole.

Bohr's quantised orbits

“An electron on a ladder can stand only on the rungs, never between them.”

Bohr postulated that only orbits with angular momentum L = n h/2π are allowed; in these stationary states the electron does not radiate. Light is emitted or absorbed only when the electron jumps between two such quantised levels. The common error is to picture continuous radiation in an allowed orbit.

Memory trick: Orbit = rung, photon = jump.

Mass defect and binding energy

“When hydrogen nuclei fuse into helium, a flash of light shows that some mass vanished as energy.”

A bound nucleus weighs less than the sum of its separate protons and neutrons; the missing mass Δm appears as binding energy B = Δm c². Exam trap: always subtract nucleus mass from the sum of nucleon masses and keep the result positive.

Memory trick: Mass defect = (sum of nucleon masses) – (nucleus mass).

Accuracy, precision and uncertainty

“Hitting the same spot on a dartboard repeatedly shows precision, even if the board is misplaced.”

Accuracy = closeness to the accepted value; precision = repeatability of measurements. Random errors shrink with many trials, but a systematic calibration error remains, so a tight cluster can still be inaccurate.

Memory trick: Bull’s-eye cluster = precise; centre at true value = accurate.

Superposition

“When two water ripples meet, the surface rises higher or flattens depending on their relative phase.”

Linear superposition adds instantaneous displacements: y = y₁ + y₂. Same-phase waves give constructive interference (amplitude doubles); opposite-phase give destructive (cancellation). The trap: never add intensities before considering phase.

Memory trick: Add y first, then square for intensity.

Circular and helical motion

“A garden sprinkler sprays water upward while wind blows sideways, tracing a helix like a charge’s path with both v⊥ and v∥ in a magnetic field.”

In a uniform B, the perpendicular velocity component v⊥ makes the charge move in a circle of radius r = mv⊥/(|q|B); the parallel component v∥ remains unchanged, producing a helix whose pitch = v∥·T (T = period). Trap: using total speed instead of v⊥ for the radius.

Memory trick: r ∝ v⊥ ; pitch ∝ v∥.

Path difference & fringes

“In a double-slit experiment the central bright line appears because the two paths differ by 0 λ, and each next bright fringe adds another whole λ.”

Constructive interference (bright fringes) occurs when the path difference Δ = nλ, where n = 0,1,2,… . Destructive interference (dark fringes) occurs when Δ = (n+½)λ. A common trap is forgetting n = 0, which would miss the central bright fringe.

Memory trick: Bright: Δ = nλ (n=0,1,2…); Dark: Δ = (n+½)λ

RMS value

“A 230 V rms electric kettle heats water like a 230 V DC source, though the sinusoid peaks at 325 V.”

RMS (root-mean-square) voltage is the DC value that yields the same average heating power. For a sinusoid Vrms = Vpeak/√2 = V0/√2. Students often confuse the peak voltage with the effective value, causing incorrect power results.

Memory trick: RMS = Vpeak/√2 for sine; think ‘√2-down from peak.’

Depletion region

“The dark gap between the p-type and n-type layers in a solar cell is the depletion region, empty of free carriers.”

The depletion region is the zone around the p-n junction where free electrons and holes have recombined, leaving fixed ionised donors and acceptors. This creates an internal electric field and a built-in potential that opposes carrier motion. Trap: assuming this region contains mobile carriers; it is carrier-free.

Memory trick: Depletion = empty ‘no-go’ zone.

Parallax method

“Astronomers watch a nearby star wobble against distant constellations as Earth moves from one side of its orbit to the other.”

Parallax measures the apparent angular shift of a nearby object when observed from two positions separated by a known baseline (Earth’s 2 AU). Distance ≈ baseline / tan θ; for small angles tan θ ≈ θ (rad). The exam pitfall is using the small-angle formula when θ is not tiny, leading to over-estimate.

Memory trick: Baseline → shift → distance

Second equation of motion

“A car starting from rest accelerates at 2 m/s²; after 5 s it has travelled 25 m.”

With constant acceleration, displacement equals initial velocity times time plus half the acceleration times time squared. It is obtained by integrating v = u + at. In multi-step questions use the total time, not just a part, to avoid under-counting.

s = ut + ½at²

Memory trick: S = U·T + ½ A·T²

Linear momentum

“A moving baseball carries momentum that keeps it rolling after the bat hits it.”

Momentum p = mv combines mass and velocity into a vector quantity. It changes only when an external net force acts, and the change equals the impulse. Remember p has direction; opposite directions matter in collisions.

p = mv

Memory trick: p = m·v, keep direction in mind.

Potential energy

“Holding a water bottle 2 m above the floor stores gravitational potential energy like a tiny battery.”

Near Earth’s surface, gravitational potential energy is PE = m g h, where h is height above a chosen reference. Mass and height increase stored energy linearly. Mistake: using wrong height or forgetting the reference level.

PE = mgh

Memory trick: PE = m·g·h, height is the charge

Rolling motion energy

“A bowling ball rolling down the lane carries translational and rotational kinetic energy together.”

A rolling object has KE = ½mv² (translation) + ½Iω² (rotation). The translational speed v and angular speed ω are linked by v = rω for pure rolling. Mistake: adding only one term or using v ≠ rω, which gives wrong total energy.

KE = ½mv² + ½Iω²

Memory trick: Roll: KE = translational + rotational

Orbital velocity

“Satellites zip around Earth at ~7.8 km/s, exactly the speed given by v = √(GM/r).”

For a circular orbit of radius r, the required speed is v = √(GM/r); gravity supplies the centripetal force. Trap: assuming higher altitude needs higher speed; actually speed falls as radius increases.

v = √(GM/r)

Memory trick: v ∝ 1/√r – velocity drops as radius rises

Bernoulli's principle

“When a paper airplane glides, the air over its curved top moves faster, making pressure lower and producing lift.”

Bernoulli’s equation P + ½ρv² + ρgh = constant holds for steady, incompressible, non-viscous flow along a streamline. An increase in speed raises the kinetic term, so static pressure drops. In lift problems the ρgh term is often omitted because the wing’s height change is negligible; forgetting this can give a wrong pressure difference.

P + ½ρv² + ρgh = const

Memory trick: Fast = low P – ‘speed-up, pressure-down’

Stress and strain — common mistake

“Students often write “strain = 0.02 m” for a rod that stretched 2 mm over 10 cm, but the correct strain is 0.02 (dimensionless).”

Strain is defined as the ratio ΔL/L, so it must be unit-less. Writing strain in metres is wrong; only stress has units of pressure. In exam answers, a unit-bearing strain leads to loss of marks.

Memory trick: Strain = ΔL/L → never write metres.

Transverse vs longitudinal waves

“Shaking a rope side-to-side moves the rope up-down while the disturbance travels forward; a speaker pushes air back-forth along the sound direction.”

In transverse waves particle motion is perpendicular to wave propagation (e.g., light, string). In longitudinal waves particles oscillate parallel to propagation (e.g., sound in air). Trap: assuming sound is transverse because it can be polarized in solids; in gases it's purely longitudinal.

Memory trick: Transverse = ‘T’ for ‘Turn’ (perpendicular); Longitudinal = ‘L’ for ‘Line’ (along)