L-25: Dual Nature of Radiation and Matter
Physics — Class 12 · NIOS Code 312 · Module 7 · Source: 312_Physics_Eng_Lesson25.pdf
Dual Nature of Radiation and Matter
Light and matter exhibit both wave-like and particle-like behaviour under different conditions. This lesson covers the photoelectric effect (Einstein's photon theory), photoelectric tubes, de Broglie's matter waves, and their experimental verification. Module 7: Atoms and Nuclei.
NIOS objectives: photoelectric effect and laws; Einstein's equation; de Broglie wavelength; Davisson–Germer experiment.
25.1 Photoelectric Effect
Discovered by Hertz (1887); electrons emitted from metal when light of sufficiently high frequency falls on it — photoelectrons. Distinct from thermionic emission (electrons gain energy from heat, not photons).
Experimental Observations (Millikan)
- Kmax (hence stopping potential V₀) increases with frequency ν; independent of intensity.
- Threshold frequency ν₀ exists below which no emission occurs (material property).
- Number of photoelectrons per unit area ∝ intensity of light (at fixed ν).
- Emission is instantaneous (~10⁻⁹ s time lag).
- Saturation current reached when all emitted electrons are collected (Vs).
Work done against retarding field equals max KE
Graph V₀ vs ν: slope = h/e; x-intercept = ν₀
25.2 Einstein's Theory of Photoelectric Emission
Light consists of discrete energy bundles — photons. Photoelectric effect = collision between one photon and one bound electron.
φ₀ = hν₀ (threshold frequency)
Kmax = h(ν − ν₀) when ν > ν₀
Work functions (eV): Na 2.5, K 2.3, Zn 3.4, Fe 4.8, Ni 5.9.
Einstein explains: no emission below ν₀; Kmax linear in (ν − ν₀); higher intensity → more photons → more electrons (not higher Kmax); instantaneous transfer; ν₀ depends on material only. Millikan verified Einstein's equation and measured h.
If λ doubles, photon energy E = hc/λ halves
Doubling intensity does not change Kmax
25.3 Photoelectric Tube
Evacuated glass tube: semi-cylindrical cathode (low-work-function coating) + wire anode. Variable accelerating voltage; saturation current ~ nA, proportional to light intensity. Used in cinema sound reproduction, photo-telegraphy, burglar/fire alarms, TV cameras, traffic detectors.
25.4 de Broglie Hypothesis
If light (wave) shows particle nature (photon), matter particles should show wave nature. Symmetry argument + E = mc² reasoning.
Particle momentum p ↔ wave property λ
Converse: wave of λ has momentum p = h/λ
½mv² = qV → p = √(2qmV)
100 V electron: λ = 1.23 Å (X-ray range, ~ atomic spacing)
Macroscopic objects (cricket ball): λ imperceptibly small (~10⁻³² m for 50 g ball at 20 cm/s). de Broglie waves observable only for microscopic particles.
25.4.1 Davisson–Germer Experiment (1927)
Electron beam (controlled by accelerating voltage) incident on nickel crystal; detector at angle θ measures scattered intensity. Peak at 54 eV, θ = 50° → λ ≈ 1.67 Å — matches de Broglie prediction. First direct evidence of matter waves (electron diffraction).
25.4.2 Applications — Electron Microscope
Resolution improves with shorter wavelength. Electrons at high KE have λ much smaller than visible light → electron microscopes achieve 10,000×+ magnification vs optical limit ~1000×. TEM (1931, Knoll & Ruska): electron beam through specimen, magnetic lenses, phosphor screen — analogous to light microscope but with electrons.
DUAL NATURE — KEY POINTS
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Photoelectric : hν = φ₀ + Kmax ; emission if ν > ν₀
Stopping pot. : eV₀ = Kmax ; V₀ ∝ ν (slope h/e)
Intensity effect : more electrons, same Kmax
Photon energy : E = hν ; p = hν/c
de Broglie : λ = h/p = h/(mv)
Electron (V vol) : λ = 12.3/√V Å
Davisson–Germer : electron diffraction → matter waves
Phototube uses : cinema sound, alarms, photo-telegraphy
Quick Revision
- Classical wave theory failed: instant emission, threshold frequency, intensity independence of Kmax.
- One photon ejects at most one electron (for given frequency).
- Stopping potential graph: x-intercept ν₀, slope h/e.
- de Broglie: moving particles, not stationary ones, have matter waves.
- 100 eV electrons: λ ≈ 1.23 Å — suitable for crystal diffraction studies.
Q1. In photoelectric emission, electrons gain energy from:
Q2. Einstein's photoelectric equation is:
Q3. If the intensity of incident light is doubled (frequency fixed), Kmax of photoelectrons:
Q4. The slope of the graph between stopping potential V₀ and frequency ν is:
Q5. The work function of a metal depends on:
Q6. de Broglie wavelength of a particle is given by:
Q7. An electron accelerated through 100 V has de Broglie wavelength approximately:
Q8. Davisson–Germer experiment demonstrated:
Q9. Saturation current in a phototube depends on:
Q10. If the wavelength of electromagnetic radiation is doubled, photon energy:
PYQ — Previous Year Questions
Extracted from NIOS Physics (312) board exam papers in your PDF. Chapter L25 — Dual Nature of Radiation and Matter only. Use Model Answer for marking points; Explanation for concept clarity.
Chapter 25 — Dual Nature of Radiation and Matter (L25)
6 questions · Section B · Sources: 312/MAY/204A–C, 68/ESS/1-312-A
Section B — Short Answer (2 marks)
PYQ1. Calculate the momentum of a photon of frequency ν.
Model Answer
Photon energy E = hν
Momentum p = E/c = hν/c
Also p = h/λ where λ = c/ν
Explanation
Photons have zero rest mass but carry momentum p = hν/c — radiation pressure and Compton effect (L25 §25.1).
PYQ2. Work function for iron is 4.8 eV. Will photoemission take place if radiations of frequency 12×10¹⁴ Hz are incident on an iron cathode?
Model Answer
Photon energy: E = hν = 6.626×10⁻³⁴ × 12×10¹⁴ = 7.95×10⁻¹⁹ J
In eV: E = 7.95×10⁻¹⁹ / 1.6×10⁻¹⁹ ≈ 4.97 eV
Since E > φ₀ (4.8 eV), photoemission will occur. Kmax ≈ 0.17 eV
Explanation
Einstein condition: emission only if hν ≥ φ₀. Intensity affects photocurrent, not threshold (L25 §25.1).
PYQ3. Threshold frequency for a metal is 1.160×10¹⁵ Hz. Calculate the work function of the metal in electron volt.
Model Answer
φ₀ = hν₀ = 6.626×10⁻³⁴ × 1.160×10¹⁵ = 7.686×10⁻¹⁹ J
φ₀ = 7.686×10⁻¹⁹ / 1.6×10⁻¹⁹ ≈ 4.8 eV
Explanation
Threshold frequency ν₀ is minimum ν for photoelectric emission; work function φ₀ = hν₀ (L25 §25.1).
PYQ4. Draw a diagram to show experimental arrangement for observing the photoelectric effect.
Model Answer
Labelled diagram: evacuated glass tube; photosensitive cathode (emitter); anode/collector; monochromatic light through quartz window; variable potential difference; microammeter for photocurrent.
Light ejects photoelectrons from cathode; current measured for different frequency/intensity and retarding voltage.
Explanation
Standard Hertz–Lenard / Millikan-type setup to study Einstein's photoelectric equation (L25 §25.1).
PYQ5. Draw a plot showing the variation of photoelectric current with anode potential for two different frequencies ν₁ > ν₂ of incident radiation having the same intensity. In which case will the stopping potential be higher?
Model Answer
Two I–V curves saturating at same current (same intensity) but different stopping potentials.
Stopping potential higher for ν₁ (ν₁ > ν₂) because Kmax = hν − φ₀ increases with frequency.
Marking scheme: greater frequency → more negative stopping potential magnitude.
Explanation
Same intensity ⇒ same number of photons per second ⇒ same saturation current (for ν above threshold). Stopping potential V₀ = Kmax/e depends only on ν, not intensity (L25 §25.1).
PYQ6. Write any two applications of photocells.
Model Answer
Any two, e.g.:
- Automatic switching of street lights / exposure meters in cameras
- Burglar alarms and door-openers (light beam interrupted)
- Sound reproduction in motion pictures; solar cells (photovoltaic variant)
Explanation
Photocells convert light to electrical signal via photoelectric effect — used wherever light intensity must be detected (L25 §25.1).
Problem Solving — L25 Dual Nature of Radiation and Matter
Six problems spanning this chapter’s NIOS syllabus. Every question is built from the notes and formula sheet: solve with equations first, then read the formal textbook-style write-up, the easy explanation, and the topic in depth (formulas, meaning, exam tips). Explanations open by default.
Light of frequency f hits a metal with work function φ. Write Einstein’s equation and meaning of threshold frequency.
Solution — step by step with formulas
- hf = φ + K_max.
- f₀ = φ/h; no emission if f < f₀.
Final answer: hf = φ + K_max; f₀ = φ/h
Formulas used in this problem
Textbook formal language
Photon energy quanta explain instantaneous emission and f-dependent K_max.
Working formula set for this problem: hf = φ + K_max; K_max = eV₀. In the NIOS presentation, physical quantities must be expressed in SI units and the relevant law or definition stated before substitution. Vector quantities require an explicit choice of positive direction; scalar work and energy require attention to sign conventions of the textbook.
Easy language (same idea, plain words)
Each photon spends some energy freeing the electron; leftover is KE. Too red ⇒ no electrons.
Read the question once for the story, once for the numbers. Write the formula, plug in values with units, then simplify. If a result looks huge or tiny, re-check powers of ten and whether you used sin/cos of the correct angle.
Topic in depth — Photoelectric effect
Intensity raises number of photons, hence photocurrent, not K_max (above threshold).
Link to chapter notes (L25 — Photoelectric effect): this idea sits with the definitions and worked examples in the detailed notes and formula sheet. Memorise: hf = φ + K_max; K_max = eV₀. In multi-step questions, keep a free-body diagram or energy flow sketch before algebra; most errors are missing forces or wrong signs, not hard maths.
Exam tip
Quote the law in one line, then write hf = φ + K_max; K_max = eV₀ before numbers. Box the final answer with unit. For numericals, keep at least three significant figures until the last step unless the data are coarse.
Common mistakes
- Mixing up scalar and vector quantities (e.g. treating momentum as unsigned).
- Using the wrong sign convention for work/heat/force direction.
- Forgetting to convert units (g↔kg, cm↔m, minutes↔seconds).
- Applying a formula outside its assumptions (e.g. F = ma when mass is not constant).
If stopping potential is 2.0 V, find K_max of photoelectrons in eV.
Solution — step by step with formulas
- K_max = 2.0 eV.
Final answer: K_max = 2.0 eV
Formulas used in this problem
Textbook formal language
Stopping potential measures maximum KE via eV₀ = K_max.
Working formula set for this problem: eV₀ = K_max. In the NIOS presentation, physical quantities must be expressed in SI units and the relevant law or definition stated before substitution. Vector quantities require an explicit choice of positive direction; scalar work and energy require attention to sign conventions of the textbook.
Easy language (same idea, plain words)
Need 2 V reverse to stop the fastest electrons—so they had 2 eV KE.
Read the question once for the story, once for the numbers. Write the formula, plug in values with units, then simplify. If a result looks huge or tiny, re-check powers of ten and whether you used sin/cos of the correct angle.
Topic in depth — Stopping potential
V₀ depends on frequency, not intensity (above threshold).
Link to chapter notes (L25 — Stopping potential): this idea sits with the definitions and worked examples in the detailed notes and formula sheet. Memorise: eV₀ = K_max. In multi-step questions, keep a free-body diagram or energy flow sketch before algebra; most errors are missing forces or wrong signs, not hard maths.
Exam tip
Quote the law in one line, then write eV₀ = K_max before numbers. Box the final answer with unit. For numericals, keep at least three significant figures until the last step unless the data are coarse.
Common mistakes
- Mixing up scalar and vector quantities (e.g. treating momentum as unsigned).
- Using the wrong sign convention for work/heat/force direction.
- Forgetting to convert units (g↔kg, cm↔m, minutes↔seconds).
- Applying a formula outside its assumptions (e.g. F = ma when mass is not constant).
Find energy and momentum of a photon of wavelength 500 nm (h=6.63×10⁻³⁴, c=3×10⁸).
Solution — step by step with formulas
- E = hc/λ ≈ 3.98×10⁻¹⁹ J.
- p = h/λ ≈ 1.33×10⁻²⁷ kg·m·s⁻¹.
Final answer: E ≈ 4.0×10⁻¹⁹ J; p = h/λ
Formulas used in this problem
Textbook formal language
Photons are quantum of EM field with E = hf and p = E/c = h/λ.
Working formula set for this problem: E = hf; p = h/λ. In the NIOS presentation, physical quantities must be expressed in SI units and the relevant law or definition stated before substitution. Vector quantities require an explicit choice of positive direction; scalar work and energy require attention to sign conventions of the textbook.
Easy language (same idea, plain words)
Bluer light means punchier photons with more momentum each.
Read the question once for the story, once for the numbers. Write the formula, plug in values with units, then simplify. If a result looks huge or tiny, re-check powers of ten and whether you used sin/cos of the correct angle.
Topic in depth — Photon properties
Photon rest mass is zero; always speed c in vacuum.
Link to chapter notes (L25 — Photon properties): this idea sits with the definitions and worked examples in the detailed notes and formula sheet. Memorise: E = hf; p = h/λ. In multi-step questions, keep a free-body diagram or energy flow sketch before algebra; most errors are missing forces or wrong signs, not hard maths.
Exam tip
Quote the law in one line, then write E = hf; p = h/λ before numbers. Box the final answer with unit. For numericals, keep at least three significant figures until the last step unless the data are coarse.
Common mistakes
- Mixing up scalar and vector quantities (e.g. treating momentum as unsigned).
- Using the wrong sign convention for work/heat/force direction.
- Forgetting to convert units (g↔kg, cm↔m, minutes↔seconds).
- Applying a formula outside its assumptions (e.g. F = ma when mass is not constant).
Calculate de Broglie wavelength of an electron with speed 10⁶ m·s⁻¹ (m=9.1×10⁻³¹).
Solution — step by step with formulas
- p = mv ≈ 9.1×10⁻²⁵.
- λ = h/p ≈ 7.3×10⁻¹⁰ m.
Final answer: λ ≈ 0.73 nm
Formulas used in this problem
Textbook formal language
Material particles exhibit wave nature with λ = h/p.
Working formula set for this problem: λ = h/p = h/(mv). In the NIOS presentation, physical quantities must be expressed in SI units and the relevant law or definition stated before substitution. Vector quantities require an explicit choice of positive direction; scalar work and energy require attention to sign conventions of the textbook.
Easy language (same idea, plain words)
Faster or heavier ⇒ shorter wavelength; electrons show measurable λ in crystals.
Read the question once for the story, once for the numbers. Write the formula, plug in values with units, then simplify. If a result looks huge or tiny, re-check powers of ten and whether you used sin/cos of the correct angle.
Topic in depth — Matter waves
Davisson–Germer experiment confirmed electron diffraction.
Link to chapter notes (L25 — Matter waves): this idea sits with the definitions and worked examples in the detailed notes and formula sheet. Memorise: λ = h/p = h/(mv). In multi-step questions, keep a free-body diagram or energy flow sketch before algebra; most errors are missing forces or wrong signs, not hard maths.
Exam tip
Quote the law in one line, then write λ = h/p = h/(mv) before numbers. Box the final answer with unit. For numericals, keep at least three significant figures until the last step unless the data are coarse.
Common mistakes
- Mixing up scalar and vector quantities (e.g. treating momentum as unsigned).
- Using the wrong sign convention for work/heat/force direction.
- Forgetting to convert units (g↔kg, cm↔m, minutes↔seconds).
- Applying a formula outside its assumptions (e.g. F = ma when mass is not constant).
State wave–particle duality for light and for electrons in one sentence each.
Solution — step by step with formulas
- Light: interference (wave) and photoelectric (particle).
- Electrons: tracks/KE (particle) and diffraction (wave).
Final answer: Both show wave and particle aspects in different experiments
Textbook formal language
Quantum objects need both descriptions; classical either/or fails.
Working formula set for this problem: (see solution steps). In the NIOS presentation, physical quantities must be expressed in SI units and the relevant law or definition stated before substitution. Vector quantities require an explicit choice of positive direction; scalar work and energy require attention to sign conventions of the textbook.
Easy language (same idea, plain words)
Light and matter can act like waves or bullets depending on the experiment.
Read the question once for the story, once for the numbers. Write the formula, plug in values with units, then simplify. If a result looks huge or tiny, re-check powers of ten and whether you used sin/cos of the correct angle.
Topic in depth — Duality
Complementarity: full wave and particle pictures are mutually exclusive in one setup.
Link to chapter notes (L25 — Duality): this idea sits with the definitions and worked examples in the detailed notes and formula sheet. Memorise: (see solution steps). In multi-step questions, keep a free-body diagram or energy flow sketch before algebra; most errors are missing forces or wrong signs, not hard maths.
Exam tip
Quote the law in one line, then write (see solution steps) before numbers. Box the final answer with unit. For numericals, keep at least three significant figures until the last step unless the data are coarse.
Common mistakes
- Mixing up scalar and vector quantities (e.g. treating momentum as unsigned).
- Using the wrong sign convention for work/heat/force direction.
- Forgetting to convert units (g↔kg, cm↔m, minutes↔seconds).
- Applying a formula outside its assumptions (e.g. F = ma when mass is not constant).
Why can intense light exert pressure on a surface?
Solution — step by step with formulas
- Photons carry momentum h/λ; reflection/absorption transfers momentum ⇒ force.
Final answer: Momentum transfer from photons
Formulas used in this problem
Textbook formal language
Radiation pressure is force per area from EM momentum flux.
Working formula set for this problem: p = E/c (photon). In the NIOS presentation, physical quantities must be expressed in SI units and the relevant law or definition stated before substitution. Vector quantities require an explicit choice of positive direction; scalar work and energy require attention to sign conventions of the textbook.
Easy language (same idea, plain words)
Light punches gently with many photon kicks—strong beams can move dust in space.
Read the question once for the story, once for the numbers. Write the formula, plug in values with units, then simplify. If a result looks huge or tiny, re-check powers of ten and whether you used sin/cos of the correct angle.
Topic in depth — Radiation pressure idea
Perfect reflection transfers 2p per photon vs absorption p.
Link to chapter notes (L25 — Radiation pressure idea): this idea sits with the definitions and worked examples in the detailed notes and formula sheet. Memorise: p = E/c (photon). In multi-step questions, keep a free-body diagram or energy flow sketch before algebra; most errors are missing forces or wrong signs, not hard maths.
Exam tip
Quote the law in one line, then write p = E/c (photon) before numbers. Box the final answer with unit. For numericals, keep at least three significant figures until the last step unless the data are coarse.
Common mistakes
- Mixing up scalar and vector quantities (e.g. treating momentum as unsigned).
- Using the wrong sign convention for work/heat/force direction.
- Forgetting to convert units (g↔kg, cm↔m, minutes↔seconds).
- Applying a formula outside its assumptions (e.g. F = ma when mass is not constant).