Dual Nature of Radiation and Matter shows that light behaves both as a wave and as a stream of energy packets called photons, while moving particles like electrons also have an associated matter wave. The chapter builds from the work function and the photoelectric effect through Einstein’s photoelectric equation to de Broglie wavelength and the Davisson and Germer experiment. It is a reliably scoring NEET topic where most questions come straight from Einstein’s equation, stopping potential graphs, and de Broglie wavelength calculations.
Key Concepts
1. Photoelectric Effect
When light of sufficiently high frequency falls on a metal surface, electrons are ejected. These are called photoelectrons.
Key Observations
- Below a certain threshold frequency (ν₀), no electrons are emitted regardless of intensity
- Above ν₀, photoelectrons are emitted instantly (no time lag)
- Kinetic energy of electrons depends on frequency, not intensity
- Number of electrons (photocurrent) depends on intensity
2. Einstein’s Photoelectric Equation
KE_max = hν − φ = hν − hν₀
or: eV₀ = hν − φ
- h = Planck’s constant = 6.63 × 10⁻³⁴ J·s
- ν = frequency of incident light
- φ = hν₀ = work function (minimum energy to eject electron)
- V₀ = stopping potential
3. de Broglie Hypothesis
Every moving particle has a wave associated with it:
λ = h/p = h/(mv)
For an electron accelerated through V volts:
λ = 1.227/√V nm
The Davisson-Germer experiment confirmed matter waves by showing electron diffraction.
Solved Examples
Example 1
Light of wavelength 400 nm falls on a metal with work function 2 eV. Find the maximum KE and stopping potential.
Answer: E = hc/λ = (6.63 × 10⁻³⁴ × 3 × 10⁸)/(400 × 10⁻⁹) = 4.97 × 10⁻¹⁹ J = 3.1 eV
KE_max = 3.1 − 2 = 1.1 eV. Stopping potential V₀ = 1.1 V.
Example 2
Find the de Broglie wavelength of an electron accelerated through 100 V.
Answer: λ = 1.227/√100 = 1.227/10 = 0.1227 nm
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Important Questions for Board Exams
3-Mark
- State Einstein’s photoelectric equation and explain each term.
- What is de Broglie hypothesis? Derive the expression for de Broglie wavelength.
5-Mark
- Describe the photoelectric effect. State the laws. How does Einstein’s equation explain all observations?
Quick Revision Points
- Photoelectric effect: light → ejects electrons from metal; needs ν ≥ ν₀
- Einstein: KE_max = hν − φ; V₀ = (hν − φ)/e
- Intensity ↑ → more electrons (photocurrent ↑), NOT more KE
- Frequency ↑ → more KE of electrons
- de Broglie: λ = h/mv = h/p; electron: λ = 1.227/√V nm
- Davisson-Germer: confirmed electron waves by diffraction
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Next: Ch 12 - Atoms
Class 12 Physics – swipe through all 8 cards to understand the whole chapter.
Big Idea: Dual Nature
Light behaves as both a wave and a stream of particles, and matter does too.
Wave nature shows in diffraction; particle nature in the photoelectric effect.
- Light = photons (particle) in the photoelectric effect
- Particles (electrons) act as waves (de Broglie)
- This ‘duality’ ties the whole chapter together
Work Function (φ0)
The minimum energy needed to free one electron from a metal surface.
φ0 is a property of the metal only — not of the light shone on it.
- Caesium has a low φ0 ≈ 2.14 eV, so it emits easily
- Four emission types: thermionic, field, photoelectric, secondary
- Don’t confuse φ0 with ionisation energy of an atom
Photons: Light in Packets
Radiation travels as discrete energy bundles called photons.
h = 6.63 × 10⁻34 J·s, c = 3 × 108 m/s. Use λ in nm for the 1240 shortcut.
- Photon energy depends only on frequency, not intensity
- Brighter light of same colour = more photons, not bigger ones
- Photons are massless yet carry momentum p = h/λ = E/c
Photoelectric Effect
Light of high enough frequency instantly ejects electrons from a metal.
Below threshold frequency ν0, NO emission — however intense the light.
- Photocurrent (number of electrons) ∝ intensity
- Max KE depends on frequency, never on brightness
- Emission is instantaneous (~10⁻9 s), no time lag
Stopping Potential (V0)
The reverse voltage that just halts the fastest photoelectron.
V0 vs ν graph is a straight line with universal slope h/e.
- Raising intensity lifts saturation current, not V0
- Raising frequency raises V0, not saturation current
- Slope h/e is the same for every metal; only intercept differs
Einstein’s Photoelectric Equation
One photon gives all its energy to one electron: part escapes, rest is KE.
Most-tested idea of the chapter; won Einstein the 1921 Nobel Prize.
- Threshold: φ0 = h ν0 = h c / λ0
- With stopping potential: e V0 = h ν − φ0
- KE_max rises linearly with ν, slope exactly h
de Broglie Wavelength
Every moving particle has a matter wave set by its momentum.
λ is inversely proportional to momentum — heavy/fast objects have tiny λ.
- Accelerated charge: λ = h / √(2 m q V)
- Equal K → lighter particle has larger λ (note the √)
- Everyday objects have undetectably small λ
Electron λ & Davisson–Germer
An accelerated electron has an atom-sized wavelength you can measure.
At 100 V, λ = 0.123 nm ≈ 1.23 Å — close to crystal atomic spacing.
- Shortcut is for electrons only, not protons or alphas
- Davisson–Germer: electron diffraction off a nickel crystal
- This confirmed matter waves and completes the dual nature
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Frequently Asked Questions
It is the idea that radiation shows both wave behaviour (diffraction and interference) and particle behaviour (photons in the photoelectric effect), and that matter does the same, since every moving particle has a wave nature given by de Broglie. Neither picture alone fully describes light or particles.
Einstein’s equation is h times nu equals work function plus maximum kinetic energy, which rearranges to KEmax equals h times (nu minus nu0). It is the most tested idea in the chapter because it explains the threshold frequency, instantaneous emission, and the straight-line stopping potential versus frequency graph, and it won Einstein the 1921 Nobel Prize.
Use lambda equals h divided by p, which becomes h divided by the square root of 2 m K for kinetic energy K. For an electron accelerated through a potential V there is a NEET shortcut: lambda equals 1.227 divided by the square root of V, in nanometres, with V in volts.
Yes, it is part of the Class 12 NEET physics syllabus and is considered a high-scoring chapter because the questions are formula based and predictable. Expect roughly one to two questions, usually on Einstein’s equation, stopping potential, photon energy, or de Broglie wavelength.
The work function is the minimum energy needed to free an electron from a metal surface, measured in electron volts, while the threshold frequency nu0 is the lowest frequency of light that can cause emission. They are linked by work function equals h times nu0, so a higher work function means a higher threshold frequency.