JEE Mains Physics · Teaching notes
Dual Nature of Radiation and Matter — JEE Mains Physics
Dual Nature of Radiation and Matter has 131 past-year questions from 2021 to 2026, and 8 of them ask for a number rather than an option. A little over half are about light: what one photon carries, and the photoelectric effect read through Einstein's equation. The rest are about matter waves, and more than half of those compare two particles' wavelengths. The arithmetic is short if energies stay in electron-volts and hc is taken as 1240 eV nm. Marks are lost on what a ratio holds fixed: the same kinetic energy, the same voltage and the same wavelength give three different answers, and brighter light never changes the stopping potential.
Every subtopic, worked example, formula and trap in one printable document — answers shown, ready to share.
Subtopic notes
Photon Energy, Momentum and Threshold
20 PYQsLight comes in photons of energy hν = hc/λ and momentum h/λ; a source's power is the number of photons per second times that energy, and a photon frees an electron only if its energy beats the metal's work function.
Photoelectric Laws and Graphs
21 PYQsFrequency decides whether electrons leave and how fast the fastest ones move; intensity decides only how many leave; every photoelectric graph is read from eV₀ = hν − φ.
Einstein's Equation and Stopping Potential
32 PYQsEach photon's energy pays the work function and the rest becomes the fastest electron's kinetic energy: hν = φ + K_max with K_max = eV₀; two readings on one metal let the work function be eliminated.
de Broglie Wavelength of a Particle
24 PYQsEvery moving particle has a wavelength λ = h/p = h/√(2mK); for a charge q accelerated from rest through V it is h/√(2mqV), so the wavelength falls as the speed, the energy or the voltage rises.
Comparing de Broglie Wavelengths
34 PYQsTo compare two wavelengths, write λ = h/p and ask what is held fixed: at the same kinetic energy λ ∝ 1/√m, at the same voltage λ ∝ 1/√(mq), at the same speed λ ∝ 1/m, and the same wavelength means the same momentum.
Formula & revision sheet
11 formulas · 3 reference tables · 39 gotchas across all subtopics — the exam-eve cheat-sheet
Formula & revision sheet
11 formulas · 3 reference tables · 39 gotchas across all subtopics — the exam-eve cheat-sheet
Formulas (3)
Watch out for (9)
- At equal power, the longer wavelength sends more photons→ Photon energy and photons per second
- A power ratio is not a photon ratio→ Photon energy and photons per second
- Use the hc the paper gives→ Photon energy and photons per second
- Reflection doubles the push→ Photon momentum and the push of light
- Energy and momentum rise together→ Photon momentum and the push of light
- Recoil takes energy too→ Photon momentum and the push of light
- Brightness does not lower the threshold→ Work function, threshold frequency and threshold wavelength
- Angular frequency is 2πν→ Work function, threshold frequency and threshold wavelength
- Longest wavelength, lowest frequency→ Work function, threshold frequency and threshold wavelength
Reference tables (2)
What frequency and intensity each control in the photoelectric effect6 rows
| Quantity | Raise the frequency (above threshold) | Raise the intensity (same frequency) |
|---|---|---|
| Maximum kinetic energy | Rises linearly: hν − φ | No change |
| Stopping potential | Rises linearly: (hν − φ)/e | No change Moving the lamp farther away dims it; the stopping potential stays the same. |
| Saturation current | Set by photons per second, not by their energy | Rises in proportion |
| Whether emission happens | Starts once ν passes ν₀ | Never below ν₀, however bright |
| Delay before emission | None: emission is instant | None: emission is instant |
| Photons per second at fixed intensity | Falls, as n = IA/hν | Rises in proportion |
Reading photoelectric graphs6 rows
| Graph | Shape | Slope | Intercepts, and what shifts the graph |
|---|---|---|---|
| Stopping potential against frequency | Straight line from ν₀ upward | h/e, the same for every metal | Meets the ν-axis at ν₀ and, extended, the V₀-axis at −φ/e; a larger φ shifts it right, parallel |
| Maximum kinetic energy against frequency | Straight line from ν₀ upward | h, the same for every metal | Meets the ν-axis at ν₀ and, extended, the K-axis at −φ |
| Photocurrent against collector voltage, two intensities, one frequency | Rises, then flattens at a saturation current | Flat once saturated | Both cut off at the same −V₀; the brighter light saturates higher Same cut-off voltage means same frequency. |
| Photocurrent against collector voltage, two frequencies, one intensity | Rises, then flattens at a saturation current | Flat once saturated | The higher frequency cuts off at the more negative voltage; the saturation level is the same |
| Photocurrent against intensity | Straight line through the origin | Constant for one metal and one frequency | Stays at zero below threshold at any intensity |
| Stopping potential against intensity | Horizontal line | Zero | Its height is set by the frequency |
Watch out for (6)
- Brighter light, same stopping potential→ What frequency and intensity each control in the photoelectric effect
- Doubling the frequency more than doubles the kinetic energy→ What frequency and intensity each control in the photoelectric effect
- The collector is made negative, not the emitter→ What frequency and intensity each control in the photoelectric effect
- The slope is the same for every metal→ Reading photoelectric graphs
- The potential-axis intercept is negative→ Reading photoelectric graphs
- Lowest threshold, fastest electrons→ Reading photoelectric graphs
Formulas (3)
Watch out for (8)
- Divide ω by 2π→ Einstein's photoelectric equation for one light
- Two frequencies, use the higher→ Einstein's photoelectric equation for one light
- Volts and electron-volts are the same number→ Einstein's photoelectric equation for one light
- Subtract, do not divide→ Two wavelengths on the same metal
- A longer wavelength cannot give a larger stopping potential→ Two wavelengths on the same metal
- Doubling K is not halving λ→ Two wavelengths on the same metal
- Subtract the work function before the square root→ Comparing the maximum speeds of photoelectrons
- A speed ratio is not an energy ratio→ Comparing the maximum speeds of photoelectrons
Formulas (2)
Reference tables (1)
Evidence for matter waves7 rows
| Observation or device | What it shows | Key relation |
|---|---|---|
| Davisson–Germer experiment | Electrons scattered from a nickel crystal give a diffraction peak, so electrons behave as waves | At 54 V the peak is at 50°; the measured λ ≈ 0.165 nm matches h/p |
| Electron diffraction and interference | A beam of electrons spreads and makes fringes, like light | Fringe spacing grows with λ = h/p |
| Electron microscope | Resolves far finer detail than an optical microscope | Electron λ is a fraction of a nanometre, against 400–700 nm for light |
| Heavier particle at the same speed | Shorter wavelength, finer detail | λ = h/mv, so at equal speed λ ∝ 1/m |
| Photoelectric effect | Light arrives as particles, photons | E = hν per photon |
| Heisenberg uncertainty principle | Position and momentum cannot both be known exactly | Δx Δp ≥ h/4π |
| Everyday objects | No visible wave effects | For a large mass, h/mv is far smaller than any gap or slit |
Watch out for (8)
- λ goes as 1/√K, not 1/K→ de Broglie wavelength and how it scales
- Use the particle's own charge→ de Broglie wavelength and how it scales
- Extra energy is the change, not the new total→ de Broglie wavelength and how it scales
- The force on an electron is opposite to the field→ de Broglie wavelength of an electron in an electric or magnetic field
- A sideways electric field still changes λ→ de Broglie wavelength of an electron in an electric or magnetic field
- A magnetic field never changes λ→ de Broglie wavelength of an electron in an electric or magnetic field
- Matter waves are not electromagnetic→ Evidence for matter waves
- Diffraction means wave, photoelectric means particle→ Evidence for matter waves
Formulas (3)
Watch out for (8)
- The same voltage is not the same energy→ Comparing particles at given kinetic energies or voltages
- Read the ratio the right way round→ Comparing particles at given kinetic energies or voltages
- At the same kinetic energy, heavier means shorter→ Comparing particles at given kinetic energies or voltages
- Equal wavelengths do not mean equal energies→ Same de Broglie wavelength means same momentum
- Pieces from rest share one wavelength→ Same de Broglie wavelength means same momentum
- At the same speed, λ goes as 1/m, not 1/√m→ Same de Broglie wavelength means same momentum
- A photon's energy is pc, not p²/2m→ Comparing a particle with a photon
- Same wavelength, same momentum, different energies→ Comparing a particle with a photon
PYQ weightage by concept
14 concepts · 131 PYQs — where the marks actually sit, so you know what to drill first
PYQ weightage by concept
14 concepts · 131 PYQs — where the marks actually sit, so you know what to drill first
| Concept | PYQs | Share |
|---|---|---|
| Work function, threshold frequency and threshold wavelength | 8 | 6% |
| Photon energy and photons per second | 7 | 5% |
| Photon momentum and the push of light | 5 | 4% |
| Concept | PYQs | Share |
|---|---|---|
| What frequency and intensity each control in the photoelectric effect | 14 | 11% |
| Reading photoelectric graphs | 7 | 5% |
| Concept | PYQs | Share |
|---|---|---|
| Two wavelengths on the same metal | 14 | 11% |
| Einstein's photoelectric equation for one light | 12 | 9% |
| Comparing the maximum speeds of photoelectrons | 6 | 5% |
| Concept | PYQs | Share |
|---|---|---|
| de Broglie wavelength and how it scales | 15 | 11% |
| Evidence for matter waves | 5 | 4% |
| de Broglie wavelength of an electron in an electric or magnetic field | 4 | 3% |
| Concept | PYQs | Share |
|---|---|---|
| Comparing particles at given kinetic energies or voltages | 16 | 12% |
| Same de Broglie wavelength means same momentum | 11 | 8% |
| Comparing a particle with a photon | 7 | 5% |
Test yourself on Dual Nature of Radiation and Matter
20 past JEE Mains questions from this chapter, timed at 48 minutes and marked the way the exam marks it. You see your score and every answer the moment you finish. Free to start.