Dual nature of radiation and matter Class 12th Notes - Free NCERT Class 12 Physics Chapter 11 Notes - Download PDF

While the wave nature explains the concepts of reflection and refraction well, it fails to provide an explanation of experimental phenomena such as the photoelectric effect and the Compton effect. Hence, the theory by itself is insufficient as it contradicts the experimental results. This paved the way for the dual nature of light and the concept of quanta and photons. These theories form the foundation of modern quantum mechanics, which are valid to this day. In the NCERT Notes of Class 12 Physics Chapter 11, we understand the need for a new theory along with a detailed study of the photoelectric effect.

The experiments by Hertz, Hallwach and Lenard, the failure of wave theory, Einstein's explanation of photoelectric effect, and the revolutionary idea of the photon are discussed in the chapter Dual Nature of Matter and Radiation NCERT Notes. We also discuss the wave nature of matter, which has led to applications in modern science such as the electron microscope. The NCERT Notes for Class 12 Physics chapter 11 are a crucial first step in learning modern physics.

These notes have been prepared by experts at Careers360 for convenient learning and exam preparation. They contain clear diagrams and precise explanations in simple language that are easy to understand.

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• NCERT Solutions for Class 12 Physics Chapter 11 Dual Nature of Radiation and Matter

NCERT Notes for Class 12 Physics Chapter 11: Download PDF

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NCERT Notes for Class 12 Physics Chapter 11

The dual nature of radiation and matter Class 12 notes will help you review the chapter and obtain a better understanding of the main topics addressed. It has been structured according to the latest CBSE syllabus and is well-suited for last-minute revision.

Electron Emission

The attraction forces of the ions keep free electrons inside the metal surface. The electrons can only get out if it has enough energy to overcome the attractive pull. An electron must be supplied a certain amount of energy in order to be pulled away from the metal's surface. The work function of a metal is the minimum energy required for an electron to escape from its metal surface.

The different types of Electron Emission are-

Thermionic emission:-

The free electrons can be given enough thermal energy to allow them to come out of the metal by adding heat.

Field emission:-

Electrons can be drawn out of metal by applying a very powerful electric field (of the order of 108 V m–1), as in a spark plug.

Photo-electric emission:-

Electrons are emitted when an appropriate frequency of light strikes a metal surface. Photoelectrons are electrons that are created by light.

Photoelectric Effect

Electrons are emitted from metallic surfaces when they are irradiated by electromagnetic radiation. This phenomenon is known as The Photoelectric Effect.

The electrons in the metal escape the pull of ions in the metal by absorbing energy from incident electromagnetic radiation.

Hertz’s Observation

Heinrich Hertz discovered in 1887 that when light strikes a metal surface, some electrons close to the surface acquire enough energy from the incident radiation to overcome the pull of the positive ions in the surface's substance. He did this in his study of the production of EM waves by spark discharge. He observed that the sparks were enhanced when the emitter plate was illuminated by UV light.

He concluded that the electrons escape from the metal's surface into the surrounding space after obtaining enough energy from the incoming light.

Hallwachs’ and Lenard’s Observations

Hallwachs and Lenard studied the photoelectric effect in detail between the years 1886 and 1902.

Lenard observed that when light was shown on an emitter plate between two electrodes, current started to flow. Both of them studied the variation of this photocurrent with collector plate potential, intensity of light and frequency of light. Furthermore, Hallwach observed that zinc plates became positively charged when exposed to UV light. This confirmed that negatively charged particles were emitted.

Through their study, they discovered that there is a minimum frequency of light, named as the threshold frequency, below which no electrons are emitted, through a series of tests. This frequency varied from metal to metal.

Experimental Study of Photoelectric Effect

The following items make up the experimental setup:

The photosensitive plate (emitter) and the metal plate (collector) in an evacuated tube allow electrons to flow easily from emitter to collector without encountering any air resistance.

To absorb visible light and emit electrons, a photosensitive plate (emitter) is used.
A metal plate (collector) receives electrons released by the emitter, forming a photoelectric current flow from the collector to the emitter plate (opposite to the flow of electrons)

Short-wavelength monochromatic light (meaning high frequency)

Through a potential difference, a battery is used to accelerate emitted electrons.

Photoelectric current flow causes a potential difference between the emitter and collector plates, which can be measured with a voltmeter.

Photoelectric current is measured with an ammeter.

Effect of Intensity of Light on Photocurrent

The number of photoelectrons emitted per second is directly proportional to the photocurrent. This means that the rate at which photoelectrons are emitted is proportional to the intensity of incident energy.

Effect of Potential on Photoelectric Current

The stopping potential of incident radiation is independent of its intensity for a given frequency. In other words, photoelectrons' maximum kinetic energy is dependent only on the light source and the material of the emitter plate.

The cut-off or stopping potential in the above figure for a certain frequency of incident radiation is the least negative (retarding) potential V₀ applied to plate A for which the photocurrent ends or becomes zero.

Effect of Frequency of Incident Radiation on Stopping Potential

The higher the frequency of incident light, the higher the photoelectrons' maximum kinetic energy. As a result, we'll need more retarding power to completely stop them.

The graphic above depicts the variation of photoelectric current with collector plate potential for various frequencies of incoming radiation.

$KE_{max} = eV_0$

Above a threshold frequency, the stopping potential is proportional to the incident frequency of light. The following graph shows the variation of stopping potential V0 with incident radiation frequency v for different photosensitive materials.

We can make the following conclusions from these observations-

1. The maximum kinetic energy of electrons varies linearly with frequency and is independent of intensity.
2. There exists a minimum frequency below which no photoelectric effect emission occurs.

Photoelectric Effect and Wave Theory of Light

The wave picture of light was used to explain interference, diffraction, and polarisation.

The experimental investigation of the photoelectric effect, on the other hand, cannot be described using the wave theory of light. According to the wave theory, electrons should continuously absorb radiant energy. More the intensity, more is the amplitude of electric and magnetic fields and hence a greater kinetic energy of electrons.

The wave model fails to describe the most fundamental characteristics of photoelectric emission.

As a result, a new hypothesis called the photon picture of light was presented to explain the photoelectric effect.

Einstein’s Photoelectric Equation: Energy Quantum of Radiation

To explain the photoelectric effect, Albert Einstein presented a radical new model of electromagnetic radiation (quanta of energy of radiation) in 1905. The energy of each quantum of radiant energy is hv, where h is Planck's constant and v is the light frequency.

An electron absorbs a quantum of energy (hv) of radiation in the photoelectric effect.

If the amount of energy absorbed is more than the minimal amount of energy required for the electron to escape from the metal surface, the electron is expelled with the maximal kinetic energy given by
$K_{max} = h \nu - \phi_0$

This is known as Einstein's Photoelectric Equation.

The value of the work function for a given material is constant and is determined by the substance's nature.

Kinetic Energy of Photoelectron

As $K_{max} = h \nu - \phi_0$ or $K_{max} \propto \nu $ . The photoelectron's kinetic energy is proportional to the frequency of incident light. It is unaffected by the intensity of the radiation.

Threshold frequency

Since kinetic energy cannot be negative, for a given photosensitive material, there is a minimum cut off frequency vo for which the stopping potential is zero. This minimum cut off frequency vo is referred to as threshold frequency.

$\nu = \frac{\phi_0}{h}$

Stopping Potential

This is the minimum reverse potential to stop the flow of electrons.

$K_{max} = eV_0$

From the photoelectric equation,

$V_0 = \frac{h}{e} \nu - \frac{\phi_0}{e}$

From the above equation, we can conclude, $V_0$ vs $\nu$ curve is a straight line, and the slope ($\frac{h}{e}$) is independent of the material. Using this and further experimental results, which determined the value of $e$, the value of Planck's constant ($h$) was determined.

$h = 6.626 \times 10^{-34} \mathrm{~Js}$

Intensity of Light

The amount of photons present in light determines its intensity. The frequency of incident light has no bearing on it.

Photoelectric Current and Frequency of Incident Light

Photoelectric Current is the rate at which photoelectrons are emitted from a metal surface.It has a direct relationship with the amount of incident radiation.

The photoelectrons emitted in the photoelectric effect are solely dependent on the intensity of light. If $\nu > \nu_0$, it is independent of the frequency of incident light.

Particle Nature of Light: The Photon

The Photon Theory Of Light , proposed by Albert Einstein in the early 20th century, posits that light is composed of discrete packets of energy known as photons. This theory was a significant departure from the classical wave theory of light, which described light as a continuous wave.

1. A photon is a packet of energy or particles of light that travels at the speed of light in a straight line.
   $c = 3 \times 10^{8} \mathrm{m/s}$
   $c = \lambda \nu$
2. The energy of a photon is given as $E=h \nu$, and it depends on the frequency and it does not change with a change in medium.
3. The momentum of the photon is given as $p=\frac{h}{\lambda}$
4. All photons of light of a given frequency or wavelength have the same energy or momentum, irrespective of light intensity.
5. Photons are electrically neutral and not affected by electric and magnetic fields.
6. Photons travel at the speed of light,
7. Photons can interact with other particles like electrons(Compton effect) and transfer its energy. During the photon-electron collision, the momentum and total energy are conserved.
8. The dynamic mass of the photon is m = E/c², where E is the energy of the photon

Wave Nature of Matter

Interference, diffraction, and polarisation are all examples of light's wave nature. Radiation also behaves as if it were made up of a bunch of particles – the photons – in the photoelectric and Compton effects, which involve energy and momentum transfer.

A logical question arises: If radiation has a dual (wave-particle) nature, don't natural particles (electrons, protons, etc.) have wave-like properties as well?
Matter, according to the de Broglie hypothesis, has a wave-like quality.

If radiation has two sides, then matter should as well.

According to De Broglie, a moving material particle can be associated with a wave. De Broglie proposed that the wavelength, $\lambda$​ associated with a moving material particle of momentum $p$ is given as

$\lambda=\frac{h}{p}$

The above equation shows the wave nature of matter.

Furthermore, we can write De-Broglie wavelength as

$\lambda=\frac{h}{p}=\frac{h}{m v}=\frac{h}{\sqrt{2 m K}}$

Where,
$\begin{aligned}
& h= 6.626 \times 10^{-34} \mathrm{Js} = \text { Plank's constant } \\
& m=\text { Mass of particle } \\
& v=\text { Speed of the particle } \\
& K=\text { Kinetic energy of particle }
\end{aligned}$

Davisson and Germer’s Experiment

The Davisson-Germer Experiment provides experimental proof of the concept of the material particle-wave nature.

Davisson and Germer's experimental setup is schematically depicted in the diagram below:

An electron gun was utilised to create a beam of electrons in the experiment.

This tiny beam of accelerated electrons was directed into a nickel crystal, where the crystal's atoms scattered the electrons in various ways.

A detector measured the intensity of the electron beam dispersed in a certain direction.

On a circular scale, this detector was designed to rotate.

As a result of the experiment, scientists examined the intensity of scattered electron beams at various latitude angles or scattering angles, which are the angles between the incident and scattered electron beams. The accelerating voltage was varied from 44 to 68 V during the experiment.

For an accelerating voltage of 54v and a scattering angle of θ=500, a high peak in the intensity (I) of the scattered electron was observed.

The constructive interference of electrons scattered from distinct layers of the regularly spaced atoms of the crystals causes the peak to appear in a specific direction.

The wavelength of matter waves was determined by electron diffraction studies to be 0.165 nm.

Dual Nature of Radiation and Matter Previous Year Question and Answer

Q.1 Using a photon picture of light, show how Einstein’s photoelectric equation can be established. Write two features of the photoelectric effect that cannot be explained by wave theory.

Answer:

In the photoelectric effect, electrons absorb a quantum of energy $(h v)$, and if it exceeds the threshold frequency required for an electron to escape from the metal surface, then the electron is emitted with maximum kinetic energy.
$K_{\max }=h v-\phi_o$ (Einstein's photoelectric equation)
Wave theory cannot explain
i) that the photoelectric effect is instantaneous
ii) that the maximum kinetic energy is independent of the intensity of incident light.

Q.2 The maximum kinetic energy of the photoelectrons emitted is doubled when the wavelength of light incident on the photosensitive surface changes from $\lambda_1$ to $\lambda_2$. Deduce expressions for the threshold wavelength and work function for the metal surface in terms of $\lambda_1$ and $\lambda_2$.

Answer:

$\begin{aligned}
& K_{\max }=\frac{h c}{\lambda_1}-\phi_0=h c\left(\frac{1}{\lambda_1}-\frac{1}{\lambda_0}\right) \quad \ldots (i)\\
& 2 K_{\max }=h c\left(\frac{1}{\lambda_2}-\frac{1}{\lambda_0}\right) \quad \ldots (ii)\\ \\
&\text{Dividing (i) with (ii)} \\
& \frac{K_{\max }}{2 K_{max}}=\frac{\left(\frac{1}{\lambda_1}-\frac{1}{\lambda_0}\right)}{\left(\frac{1}{\lambda_2}-\frac{1}{\lambda_0}\right)} \\
&\implies \lambda_0=\frac{\lambda_1 \lambda_2}{2 \lambda_2-\lambda_1} \\ \\
& \text{Work Function is given as, }\\
& \phi_0=\frac{h c}{\lambda_0}=\frac{h c\left(2 \lambda_2-\lambda_1\right)}{\lambda_1 \lambda_2}\end{aligned}$

Q.3 The work function of aluminium is 4·2 eV. If two photons each of energy 2·5 eV are incident on its surface, will the emission of electrons take place? Justify your answer.

Answer:

If the two photons each of energy 2.5 eV are incident on the given surface, then the emission of electrons will not take place. This is because the energy $h \nu$, of a single photon, is less than the work function $\phi_o$

$\because K_{\max }=h \nu-\phi_o$

If $h \nu<\phi_o$, no emission will take place.

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