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Physics notesOptics & ModernPhotoelectric & Bohr

Independent topic page

Photoelectric Effect & Bohr Model

Write K_max = hν − φ before any graph talk; for Bohr use E_n = −13.6 Z²/n² eV and take transition differences for photons — keep intensity myths and one-electron limits explicit.

Portion Optics & ModernFocus Reliable Modern marks — Einstein equation and H-like Bohr; Advanced may blend graphs with series limitsTarget 60–90sPortion share 6.8%Trend Stable
Photoelectric effect and Bohr hydrogen-like atoms are paired modern pillars and often appear as concept-driven Modern Physics. Advanced mixes stopping-potential graphs with series limits and Z-scaling. Keep particle-photon energy and one-electron Bohr formulas on separate rails from many-electron chemistry habits. Modern starter template: photon energy in one unit system → photoelectric or Bohr branch → convert only at the end. Intensity never buys K_max.

How Advanced asks this

  • K_max, V_0, φ from frequency/wavelength data
  • Photoelectric graph intercepts and intensity effects
  • Bohr transition λ, energy or series-limit wavelength
  • Which series / longest-shortest wavelength in a set
  • H-like ion comparisons with Z scaling
  • Multi-correct: intensity vs K_max myths mixed with Bohr statements

Traps that leak marks

  • Claiming brighter light raises stopping potential
  • Using Bohr energies for multi-electron atoms
  • Attaching λ to one level instead of a transition
  • Mixing eV and joules in one equation
  • Forgetting Z² in H-like ions like He⁺, Li²⁺
  • Letting intensity raise K_max
  • Using Bohr formulas for multi-electron atoms
  • Energy-unit mismatch mid-calculation (eV mixed with J)

01. Einstein: hν = φ + K_max; K_max = e V_0. Intensity changes number of photoelectrons (sat current), not K_max, above threshold.

02. Threshold ν₀ = φ/h; for ν<ν₀, no emission regardless of intensity (ideal photoelectric).

03. Bohr H-like: E_n = −13.6 Z²/n² eV; r_n = a₀ n²/Z. Photons carry |E_i − E_f| — never quote a single level as a photon energy.

04. Spectral series: Lyman to n=1, Balmer to n=2, etc.; 1/λ = R Z²|1/n_f² − 1/n_i²|.

05. Graph literacy: V_0 vs ν has slope h/e and intercept ν₀; intensity changes the current plateau, not the intercept.

06. Photoelectric: E=hf=φ+K_max with K_max=eV₀. Intensity changes photon arrival rate (current), not K_max, above threshold. Below threshold, no electrons regardless of intensity.

07. Einstein graph: V₀ vs f has slope h/e and intercept φ/e. Work function and threshold are material properties—wavelength threshold λ₀=hc/φ.

08. Bohr H-like: E_n=−13.6 Z²/n² eV; transitions ΔE=hf. Energy units: keep eV for level differences and convert to joule only for SI formulas—stamp the unit on every energy line.

Official · 2026

Syllabus for this topic

Official syllabus points for Photoelectric Effect & Bohr Model only — not the full Optics & Modern portion map. Portion hub: Optics & Modern · Modern Physics analysis.

Syllabus on this page is topic-scoped: Photoelectric Effect & Bohr Model. The parent portion (Modern Physics) also covers other topics — use the portion hub for the full map.

Must cover (this topic)

  • Photoelectric + Bohr

Gaps / watch-outs

No topic-specific exclusions flagged — finish the unit points below for Photoelectric & Bohr.

Source: https://jeeadv.ac.in/documents/jee-advanced-2026-syllabus.pdf

Unit 01

Photoelectric Effect & Bohr Model

high

Exam focusPhotoelectric effect and Bohr hydrogen model.

Syllabus points

  • Photoelectric effect; Bohr hydrogen-like atoms

Do / check

  • Write Einstein photoelectric equation before graphing

Full Physics syllabus →

Cross-topic stems

Mixed joins for this topic

Advanced rarely asks a chapter in isolation. These are tagged multi-idea Physics stems that touch Photoelectric Effect & Bohr Model — practise the knowledge bridge, not only the single-chapter drill.

Physics2023 · Paper 1 · Q8–Q10numerical

Modern Physics NUM + ray optics NUM chain

Modern Physics+Ray optics+Linked-style numericals

Knowledge bridge

Step 1: finish photoelectric/nuclear arithmetic cleanly. Step 2: switch to ray-optics formulae (mirror/lens/prism) without reusing constants wrongly. Step 3: track significant figures as required by the grid.

Why it feels hard

Formula-dense corridor; one wrong sign convention costs two questions.

What to practise

Keep a tiny optics sign-convention sticky note on your desk during NUM practice.

2023 year review →Physics notes →Quick card →Syllabus →

All mixed joins →

Why methods matter

Common methods that change your score

Einstein before graphs; Bohr photons are level differences — intensity never changes K_max above threshold.

01

Einstein line first

Slope h/e, intercept ν₀, and intensity myths become obvious.

Do thisAlways write hν=φ+K_max before reading a V_0–ν graph.

Why it works

Slope h/e, intercept ν₀, and intensity myths become obvious.

See it once

Higher intensity → higher sat current; same ν → same V_0.

02

Unit bridge

Stops φ in eV mixed with h in J·s mid-line.

Do thisConvert everything to eV or everything to J once; use hc=12400 eV·Å when handy.

Why it works

Stops φ in eV mixed with h in J·s mid-line.

See it once

E(eV)=12400/λ(Å) for photons.

03

Transition difference

Kills ‘wavelength of n=2 orbit’ distractors.

Do thisPhoton energy is |E_i−E_f|, never a single level’s E_n alone.

Why it works

Kills ‘wavelength of n=2 orbit’ distractors.

See it once

n=3→2: ΔE=13.6 Z²(1/4−1/9) eV.

04

Z-scaling ratios

Ratio questions finish without Rydberg constants.

Do thisFor H-like comparisons, factor Z² out of energies and 1/Z out of radii before numbers.

Why it works

Ratio questions finish without Rydberg constants.

See it once

E∝Z²/n²; λ∝1/(Z² Δ(1/n²)).

Processed examples

Sample questions · full working

Read the impact line first. Then notice which family/model was chosen. The solution is written the way your rough sheet should look in the hall.

01

bankFamily · Einstein photoelectric equation

Sample question

Work function is 2 eV. Light of wavelength 400 nm is incident. Find K_max. Take hc=1240 eV·nm.

This stem rewards early recognition of the einstein photoelectric equation model.

Model chosenK_max=hc/λ−φ.

Processed solution

  1. hc/λ=3.1 eV.
  2. K_max=1.1 eV.

Answer1.1 eV

Takeaway: Convert wavelength before subtracting φ.

02

standardFamily · Bohr hydrogenic levels

Sample question

Find the energy of the photon emitted in H atom for n=2→1.

This stem rewards early recognition of the bohr hydrogenic levels model.

Model chosenΔE=13.6(1−1/4) eV.

Processed solution

  1. ΔE=10.2 eV.

Answer10.2 eV

Takeaway: Use level differences, not a single-level energy.

03

twistFamily · Bohr hydrogenic levels

Sample question

Find the shortest wavelength in the Paschen series of He⁺ (Z=2).

This Advanced-level variation couples hidden constraints with the bohr hydrogenic levels model.

Model chosenPaschen: n_f=3; shortest ⇒ n_i→∞.

Processed solution

  1. ΔE_max=13.6 Z²(1/3²−0)=13.6×4/9 eV.
  2. λ=hc/ΔE with hc≈12400 eV Å.
  3. λ=12400/(13.6×4/9)=12400×9/(54.4) Å.
  4. λ≈2050 Å.

Answer≈2050 Å

Takeaway: Series limit is the n→∞ transition to the series’ lower level.

Reusable models

Common question families

Advanced stems cluster. Name the family in 10–15s, write the fast model, then run the same path. Do not invent a new plan each time.

01

Einstein photoelectric equation

Looks likeK_max=hν−φ; stopping potential eV₀=K_max

Fast modelPlot/interpret V₀ vs ν with slope h/e.

Same solve path

  1. Convert λ or ν.
  2. Write K_max=hc/λ−φ.
  3. Find V₀=K_max/e.
  4. Check threshold ν₀=φ/h.

Rough skeleton

  • ν,φ
  • K_max
  • V₀

Why faster

Recognition fixes the model before arithmetic begins.

Refuse this

Do not start blind expansion or casework before identifying the governing model.

02

Intensity and saturation current

Looks likePhotocurrent vs intensity/frequency

Fast modelIntensity → photon rate → saturation current; frequency → K_max.

Same solve path

  1. Separate intensity effects from frequency effects.
  2. Saturation current ∝ intensity (above threshold).
  3. K_max independent of intensity.
  4. Answer graphs qualitatively.

Rough skeleton

  • I vs ν split
  • i_sat
  • K_max

Why faster

Recognition fixes the model before arithmetic begins.

Refuse this

Do not start blind expansion or casework before identifying the governing model.

03

Bohr hydrogenic levels

Looks likeE_n=−13.6 Z²/n²; transitions

Fast modelPhoton energy = |E_i−E_f|; series from final n.

Same solve path

  1. Identify Z and n_i, n_f.
  2. Compute ΔE.
  3. Find λ=hc/|ΔE|.
  4. Name series if asked.

Rough skeleton

  • levels
  • ΔE
  • λ

Why faster

Recognition fixes the model before arithmetic begins.

Refuse this

Do not start blind expansion or casework before identifying the governing model.

04

Bohr radius and angular momentum

Looks liker_n∝n²/Z; L=nħ

Fast modelUse quantized L and Coulomb balance for r,v.

Same solve path

  1. Write L=nħ.
  2. Use mvr and Coulomb force balance.
  3. Find r_n, v_n.
  4. Scale with Z and n.

Rough skeleton

  • quantum L
  • balance
  • r,v

Why faster

Recognition fixes the model before arithmetic begins.

Refuse this

Do not start blind expansion or casework before identifying the governing model.

Hall timing

60–90s process

  1. 0–15s
    Classify photoelectric (Einstein) vs Bohr H-like spectrum/orbit.

    Underline optical elements or modern-physics mode (ray, YDSE/diffraction/polarisation, photoelectric, Bohr, X-ray, nuclear). Note the exact ask and any sign-convention figure.

  2. 15–35s
    Photoelectric: convert λ→ν or E; write hν=φ+K_max. Bohr: write Z, n_i, n_f and ΔE.

    Write the governing relation once: mirror/lens formula with signs, path difference, Einstein equation, Bohr ΔE, Moseley/de Broglie, or decay law. Reject out-of-syllabus interference setups beyond YDSE.

  3. 35–75s
    Solve V_0, φ, λ or ratio; keep eV and J conversions explicit.

    Compute with one consistent convention and units (eV vs J, nm vs m). Carry magnification signs and decay exponents carefully.

  4. 75–90s
    Check threshold logic, intensity vs K_max myth, and one-electron applicability of Bohr.

    Check limits (thin lens, small angle, λ≪a), energy/sign sense and syllabus scope. Multi-correct: test each statement alone.

After the model is locked

Quick formula bank

Einstein equation

hν = φ + K_max; K_max = e V_0

Photoelectric effect

Threshold

ν₀ = φ/h; λ₀ = hc/φ

Cut-off frequency/wavelength

Photon energy

E = hν = hc/λ

EM quantum energy

Bohr energy

E_n = −13.6 Z²/n² eV

Hydrogen-like ion

Bohr radius

r_n = 0.529 n²/Z Å

H-like orbit radius

Rydberg

1/λ = R Z²(1/n_f² − 1/n_i²)

Emission/absorption lines

hc handy

hc ≈ 12400 eV·Å

Fast λ↔E in eV

Mental bank

  • hν = φ + K_max
  • V_0 = K_max/e
  • Intensity ≠ K_max (above threshold)
  • E_n = −13.6 Z²/n² eV
  • Photon ↔ |ΔE|
  • hc ≈ 12400 eV·Å
  • Lyman → n=1; Balmer → n=2
  • hf=φ+K_max; K_max=eV₀
  • Intensity → photocurrent; f → K_max
  • E_n=−13.6 Z²/n² eV (H-like)
  • Stamp eV vs J on every energy equation

Make it automatic

Practice · checklist

Daily

  • Two photoelectric Einstein numericals and two Bohr ΔE→λ.
  • One V_0–ν graph intercept interpretation.

Weekly

  • Mixed H-like ion ratio sheet.
  • Statement drill: intensity, threshold, series limits.

100% checklist

  • Einstein equation written
  • Threshold checked
  • Intensity vs K_max separated
  • Bohr one-electron validity checked
  • Transition levels identified
  • Z scaling included
  • eV/J and Å/m consistent
  • Threshold and φ handled before K_max
  • H-like applicability checked for Bohr
  • Energy units consistent (eV ledger or full SI)
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