CBSE Class 12 Physics Revision Notes Chapter 11: Dual Nature of Radiation and Matter

Light behaves like a wave in interference and diffraction but acts like a stream of photons during energy transfer. Moving material particles also have an associated wavelength known as the de Broglie wavelength.

Dual Nature of Radiation and Matter explains why light and matter cannot be described using only classical wave or particle ideas. The photoelectric effect establishes the particle nature of light, while the de Broglie hypothesis assigns wave properties to moving particles.

Use these CBSE Class 12 Physics Revision Notes Chapter 11 for the 2026–27 session. Begin with electron emission and experimental observations. Then revise Einstein’s photoelectric equation, photon properties and matter waves.

Key Takeaways

• Work function: Minimum energy required to remove an electron from a metal surface.
• Photoelectric equation: Kmax = hν − ϕ₀ relates photon energy to electron kinetic energy.
• Photon momentum: p = h/λ even though a photon has no rest mass.
• Matter wavelength: λ = h/p gives the de Broglie wavelength of a moving particle.

Access Class 12 Physics Chapter 11 Dual Nature of Radiation and Matter Notes in 30 Minutes

Divide the chapter into three revision blocks:

• First 10 minutes: Electron emission, work function and photoelectric-effect observations
• Next 10 minutes: Intensity, frequency, stopping potential and Einstein’s equation
• Final 10 minutes: Photon properties, de Broglie hypothesis and matter waves

While solving numericals, convert electron volts into joules only when required. Also remember that intensity controls the number of emitted electrons, while frequency controls their maximum kinetic energy.

Need help revising photoelectric graphs, stopping-potential questions and de Broglie formulas?
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Electron Emission in Class 12 Physics Chapter 11 Notes

Metals contain free electrons that move within the material and produce electrical conductivity.

These electrons cannot normally escape from the surface. When an electron tries to leave, the metal becomes positively charged and attracts it back.

Work Function

The minimum energy required to remove an electron from the surface of a metal is called its work function.

It is represented by:

ϕ₀

The work function depends on:

• Nature of the metal
• Condition of the metal surface
• Surface impurities
• Surface treatment

It is generally measured in electron volts.

1 eV = 1.602 × 10⁻¹⁹ J

A metal with a smaller work function releases electrons more easily.

Types of Electron Emission

Electrons can be emitted from a metal surface through different processes.

Thermionic Emission

In thermionic emission, the metal is heated.

Thermal energy is supplied to the electrons. Electrons with sufficient energy overcome the surface attraction and escape.

Field Emission

In field emission, a very strong electric field is applied near the metal surface.

The field pulls electrons out of the metal.

The electric field required may be of the order of:

10⁸ V/m

Photoelectric Emission

In photoelectric emission, light of suitable frequency falls on a metal surface.

Electrons absorb energy from the incident light and escape from the surface. These emitted electrons are called photoelectrons.

Photoelectric Effect in Dual Nature of Radiation and Matter Class 12 Notes

The photoelectric effect is the emission of electrons from a metal surface when electromagnetic radiation of suitable frequency falls on it.

The emitted electrons are called photoelectrons.

The current produced by these electrons is called photocurrent.

Photosensitive Materials

Different metals respond to different frequencies of light.

Metals such as:

• Zinc
• Cadmium
• Magnesium

generally require ultraviolet light.

Alkali metals such as:

• Lithium
• Sodium
• Potassium
• Caesium
• Rubidium

may emit electrons even when visible light falls on them.

This happens because alkali metals generally have smaller work functions.

Hertz’s Observations in Physics Chapter 11 Revision Notes

Heinrich Hertz observed the photoelectric phenomenon in 1887 during experiments on electromagnetic waves.

He noticed that sparks across a detector loop became stronger when ultraviolet light fell on the emitter plate.

This suggested that ultraviolet light helped charged particles escape from the metal surface.

The particles were later identified as electrons.

Hertz’s observation provided an early indication that light could transfer energy to electrons in a metal.

Hallwachs and Lenard Observations in CBSE Class 12 Physics Chapter 11 Notes

Wilhelm Hallwachs and Philipp Lenard studied photoelectric emission in greater detail.

Hallwachs’ Observations

Hallwachs connected a negatively charged zinc plate to an electroscope.

When ultraviolet light fell on the zinc plate:

• The negatively charged plate lost its charge.
• An uncharged plate became positively charged.
• A positively charged plate became more positively charged.

These results showed that negatively charged particles were leaving the metal.

Lenard’s Observations

Lenard used an evacuated glass tube containing:

• A photosensitive emitter plate
• A collector plate
• An external electric circuit

When ultraviolet radiation fell on the emitter:

• Electrons were emitted.
• They moved towards the positive collector.
• A current flowed in the external circuit.

When the light was switched off, the current stopped.

Threshold Frequency

Hallwachs and Lenard found that no photoelectrons were emitted below a certain minimum frequency.

This minimum frequency is called the threshold frequency.

It is represented by:

ν₀

Threshold frequency depends on the metal.

Even highly intense light cannot cause photoemission when:

ν < ν₀

Experimental Study of Photoelectric Effect in Class 12 Physics Dual Nature Notes

The experimental arrangement contains an evacuated quartz tube with two metal plates.

• C is the photosensitive emitter.
• A is the collector.
• A battery controls their potential difference.
• A microammeter measures photocurrent.
• A voltmeter measures the applied potential.

A quartz window is used because quartz allows ultraviolet radiation to pass.

The experiment studies the effect of:

• Intensity of incident light
• Frequency of incident light
• Collector potential
• Nature of the emitter material

Effect of Light Intensity on Photocurrent Revision Notes

Keep the frequency and collector potential fixed.

When the intensity of incident light increases:

• More photons fall on the metal per second.
• More electrons are emitted per second.
• Photocurrent increases.

Therefore:

Photocurrent ∝ Intensity

The relation is approximately linear when the frequency is above the threshold frequency.

What Intensity Does Not Change

For a fixed incident frequency, increasing intensity does not increase:

• Maximum kinetic energy
• Stopping potential
• Energy of each photon

Intensity changes the number of photons, not the energy carried by each photon.

Effect of Collector Potential in Chapter 11 Physics Notes

The collector plate may be made positive or negative relative to the emitter.

Positive Collector Potential

When the collector is positive:

• Photoelectrons are attracted towards it.
• Photocurrent increases.
• More emitted electrons reach the collector.

After a certain positive potential, all emitted electrons are collected.

The current then reaches a maximum value called the saturation current.

Saturation Current

Saturation current is the maximum photocurrent obtained when all emitted photoelectrons reach the collector.

It increases with light intensity because higher intensity emits more electrons per second.

Negative Collector Potential

When the collector is negative:

• Photoelectrons are repelled.
• Only more energetic electrons reach it.
• Photocurrent decreases.

At a particular negative potential, even the fastest electrons fail to reach the collector.

The photocurrent then becomes zero.

Stopping Potential in Dual Nature of Radiation and Matter Revision Notes

The minimum negative potential applied to the collector that reduces photocurrent to zero is called the stopping potential.

It is represented by:

V₀

At the stopping potential:

Kmax = eV₀

Therefore:

½mvmax² = eV₀

Here:

• Kmax is maximum kinetic energy.
• e is the magnitude of electron charge.
• vmax is the maximum speed of emitted electrons.

Stopping Potential and Intensity

For light of a fixed frequency:

• Increasing intensity increases saturation current.
• Stopping potential remains unchanged.

This means that maximum electron energy is independent of light intensity.

Stopping Potential and Frequency

As incident frequency increases:

• Photon energy increases.
• Maximum kinetic energy increases.
• A larger stopping potential is needed.

Therefore, stopping potential increases linearly with frequency.

Effect of Frequency in CBSE Class 12 Dual Nature of Radiation and Matter Notes

Keep the intensity approximately fixed and change the incident frequency.

The experiment shows:

• Higher frequency gives a larger stopping potential.
• Maximum kinetic energy increases with frequency.
• Saturation current remains nearly the same when intensity is unchanged.
• No emission occurs below threshold frequency.

The relationship between stopping potential and frequency is linear:

V₀ = (h/e)ν − ϕ₀/e

The slope of a V₀ versus ν graph is:

Slope = h/e

The intercept on the frequency axis gives the threshold frequency.

Threshold Frequency and Work Function

At the threshold frequency:

Kmax = 0

Therefore:

hν₀ = ϕ₀

Hence:

ν₀ = ϕ₀/h

The corresponding threshold wavelength is:

λ₀ = c/ν₀

Therefore:

λ₀ = hc/ϕ₀

Photoelectric emission occurs when:

ν ≥ ν₀

or:

λ ≤ λ₀

Main Experimental Laws of Photoelectric Effect

The important experimental results are:

1. For frequency above threshold, photocurrent is directly proportional to light intensity.
2. Saturation current increases with intensity.
3. Stopping potential is independent of intensity.
4. Maximum kinetic energy increases linearly with incident frequency.
5. Each metal has a definite threshold frequency.
6. No emission occurs below threshold frequency, whatever the intensity.
7. Photoelectric emission begins almost instantaneously.
8. The time lag is of the order of 10⁻⁹ s or less.

Photoelectric Effect and Wave Theory in Physics Chapter 11 Revision Notes

Classical wave theory assumes that light energy is distributed continuously over the wavefront.

According to this theory:

• Greater intensity should give each electron more energy.
• Maximum kinetic energy should increase with intensity.
• Any frequency should produce emission if the light is intense enough.
• Electrons should require time to absorb sufficient energy.

These predictions disagree with photoelectric observations.

Failure of Classical Wave Theory

The classical wave model explains interference, diffraction and polarisation but cannot explain the photoelectric effect.

Einstein’s Photoelectric Equation in Class 12 Physics Chapter 11 Notes

In 1905, Einstein proposed that electromagnetic radiation consists of discrete energy packets.

These packets are called quanta or photons.

The energy of one photon is:

E = hν

Here:

• h is Planck’s constant.
• ν is the radiation frequency.

Planck’s constant is:

h = 6.626 × 10⁻³⁴ J s

Energy Balance in Photoelectric Emission

One electron absorbs one photon.

A part of the photon energy is used to overcome the work function. The remaining energy becomes the electron’s kinetic energy.

Therefore:

hν = ϕ₀ + Kmax

Hence:

Kmax = hν − ϕ₀

This is Einstein’s photoelectric equation.

Using:

Kmax = eV₀

we get:

eV₀ = hν − ϕ₀

Since:

ϕ₀ = hν₀

the equation may also be written as:

Kmax = h(ν − ν₀)

and:

eV₀ = h(ν − ν₀)

In Terms of Wavelength

Since:

ν = c/λ

Einstein’s equation becomes:

Kmax = hc/λ − ϕ₀

or:

eV₀ = hc/λ − ϕ₀

How Einstein’s Equation Explains the Observations

Effect of Frequency

Photon energy is hν.

A higher frequency means a more energetic photon. Therefore, the emitted electron can have greater kinetic energy.

Effect of Intensity

Higher intensity means that more photons arrive per second.

Therefore:

• More electrons are emitted.
• Photocurrent increases.
• Energy per electron does not increase.

Threshold Frequency

If:

hν < ϕ₀

the electron cannot escape.

Therefore, no photoelectric emission occurs below ν₀.

Instantaneous Emission

An electron absorbs one photon in a single interaction.

It does not gradually collect energy from the whole wavefront. Therefore, emission begins almost immediately.

Important Photoelectric Graphs in Chapter 11 Physics Notes

Photocurrent Versus Light Intensity

For fixed frequency and potential:

• The graph is a straight line.
• Photocurrent increases with intensity.

Photocurrent Versus Collector Potential

At positive potentials:

• Photocurrent rises.
• It reaches saturation current.

At negative potentials:

• Photocurrent falls.
• It becomes zero at stopping potential.

For greater intensity:

• Saturation current is higher.
• Stopping potential remains the same.

Stopping Potential Versus Frequency

The graph is a straight line:

V₀ = (h/e)ν − ϕ₀/e

Its:

• Slope is h/e.
• Frequency-axis intercept is ν₀.
• Potential-axis intercept is −ϕ₀/e.

Particle Nature of Light in CBSE Class 12 Physics Chapter 11 Notes

The photoelectric effect shows that radiation transfers energy in discrete packets.

These packets are called photons.

Photon Energy

The energy of a photon is:

E = hν

Since:

ν = c/λ

we get:

E = hc/λ

Photon energy depends on frequency or wavelength.

It does not depend on light intensity.

Photon Momentum

A photon has momentum:

p = E/c

Using E = hν:

p = hν/c

Since c = νλ:

p = h/λ

A photon has:

• Energy
• Momentum
• Zero electric charge
• Zero rest mass
• Speed c in vacuum

Number of Photons

If a monochromatic source has power P and each photon has energy hν, the number of photons emitted per second is:

N = P/(hν)

Using wavelength:

N = Pλ/(hc)

A higher intensity at fixed frequency means a greater number of photons per second.

Properties of Photons in Class 12 Physics Chapter 11 Notes

The main properties of photons are:

• Photons are quanta of electromagnetic radiation.
• Each photon has energy hν.
• Each photon has momentum h/λ.
• Photons travel at speed c in vacuum.
• Photons are electrically neutral.
• They are not deflected by electric fields.
• They are not deflected by magnetic fields.
• Photon energy is independent of radiation intensity.
• Increasing intensity increases photon number.
• Energy and momentum are conserved in photon interactions.
• Photon number need not remain conserved.

A photon may be absorbed or created during interaction with matter.

Wave and Particle Nature of Radiation in Dual Nature Revision Notes

Radiation shows different behaviour in different experiments.

Wave Nature of Light

The wave nature appears in:

• Interference
• Diffraction
• Polarisation
• Reflection
• Refraction

Particle Nature of Light

The particle nature appears in:

• Photoelectric effect
• Compton effect
• Energy transfer between radiation and matter

The required model depends on the physical experiment being studied.

Wave Nature of Matter in CBSE Class 12 Dual Nature Notes

After radiation was found to possess both wave and particle characteristics, Louis de Broglie proposed that matter should also have a dual nature.

According to the de Broglie hypothesis, every moving material particle has an associated wave.

These waves are called:

• Matter waves
• de Broglie waves

De Broglie Wavelength

The wavelength associated with a particle of momentum p is:

λ = h/p

For a non-relativistic particle:

p = mv

Therefore:

λ = h/(mv)

Here:

• m is particle mass.
• v is particle speed.

Dependence of De Broglie Wavelength

The wavelength:

• Decreases as particle momentum increases.
• Decreases as mass increases.
• Decreases as speed increases.
• Does not directly depend on particle charge.
• Is significant mainly for microscopic particles.

De Broglie Wavelength and Kinetic Energy Revision Notes

For a non-relativistic particle:

K = p²/(2m)

Therefore:

p = √(2mK)

Substituting in the de Broglie relation:

λ = h/√(2mK)

Thus, wavelength decreases when kinetic energy increases.

If kinetic energy becomes four times:

λ becomes half.

If kinetic energy becomes one-fourth:

λ becomes twice.

Charged Particle Accelerated Through Potential

When a particle of charge q is accelerated through potential difference V:

K = qV

Therefore:

λ = h/√(2mqV)

For an electron:

λ = h/√(2meV)

A commonly used form is:

λ = 1.227/√V nm

or:

λ = 12.27/√V Å

Here, V is in volts and relativistic effects are ignored.

De Broglie Wavelength of a Photon

For a photon:

p = hν/c

Therefore:

λ = h/p

Substituting photon momentum:

λ = hc/(hν)

Hence:

λ = c/ν

This is the usual electromagnetic wavelength.

Thus, the de Broglie relation is also valid for photons.

Why Matter Waves Are Not Seen for Macroscopic Objects

The de Broglie wavelength is:

λ = h/(mv)

For an everyday object:

• Mass is large.
• Momentum is large.
• Associated wavelength is extremely small.

Such a wavelength is far below measurable dimensions.

For electrons and other subatomic particles:

• Mass is very small.
• Wavelength may be comparable to atomic spacing.
• Wave behaviour becomes measurable.

Dual Nature of Radiation and Matter Formula Notes

Important Terms in Class 12 Physics Chapter 11

Useful Links for Class 12 Physics