 # CBSE Class 12th Physics Notes: Dual Nature of Radiation and Matter (Part ‒ II)

CBSE chapter wise notes based on chapter 11, Dual Nature of Radiation and Matter of Class 12 Physics NCERT textbook are available in this article. These notes are important for CBSE class 12 Physics board exam CBSE chapter wise notes based on chapter 11, Dual Nature of Radiation and Matter of Class 12 Physics NCERT textbook are available in this article. These notes are continuation of CBSE Class 12th Physics Notes: Dual Nature of Radiation and Matter (Part ‒ I).

In part I, we have studied about electron emission, methods of electron emission, photoelectric effect, Hertz’s observation, Hallwachs’ & Lenard’s observations and experimental study of photoelectric effect etc. Now in part II we will study about the topics given below

 Photoelectric Effect and Wave Theory of Light Photon Einstein’s Photoelectric Equation: Energy Quantum of Radiation Threshold frequency Intensity of Light Kinetic Energy of Photoelectron Number of Photoelectrons Emitted Photoelectric Current Einstein Photoelectric Equation and Stopping Potential Photoelectric Cell Wave Nature of Matter Davisson’s and Germer’s Experiment

The complete notes are given below

Photoelectric Effect and Wave Theory of Light

The phenomena of interference, diffraction and polarisation were explained by the wave picture of light. But the experimental study of photoelectric effect cannot be explained with the help of wave theory of light. The wave picture is unable to explain the most basic features of photoelectric emission. So, photon picture of light (a new theory) was proposed to explain the phenomenon of photoelectric effect.

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Photon

Photon is a packet of energy or quanta of energy associated with electromagnetic radiation. The energy of a photon is given by E = h v, where, v is frequency associated with photon and h is Planck’s constant.

Einstein’s Photoelectric Equation: Energy Quantum of Radiation

In 1905, Albert Einstein proposed a radically new picture of electromagnetic radiation (quanta of energy of radiation) to explain photoelectric effect.

Each quantum of radiant energy has energy , where h is Planck’s constant and v is the frequency of light.

In photoelectric effect, an electron absorbs a quantum of energy (hv) of radiation. If this quantum of energy absorbed exceeds the minimum energy needed for the electron to escape from the metal surface (work function ϕ0), the electron is emitted with maximum kinetic energy given by

Kmax = h vϕ0

The value of work function for a particular material is constant and it depends on nature of material.

Threshold frequency

For a given photosensitive material, there is a certain minimum cut off frequency vo for which stopping potential is zero this minimum cut off frequency vo is known as threshold frequency.

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Intensity of Light

Intensity of light depends upon the number of photons present in it. It does not depend on the frequency of incident light.

Kinetic Energy of Photoelectron

Kinetic energy of photoelectron depends on frequency of incident light as Kmax = h vϕ0 or Kmax v. It does not depend on intensity of radiation.

Number of Photoelectrons Emitted & Frequency of Incident Light

In photoelectric effect, photoelectrons emitted depend only on the intensity of light. It is independent of the frequency of incident light, provided v > vo.

Photoelectric Current

Photoelectric Current is defined as the rate of emission of photoelectrons from the metal surface. It is directly proportional to the intensity of incident radiation.

Einstein Photoelectric Equation & Stopping Potential

Stopping potential is the minimum retarding potential which should be applied across a photoelectric tube in order to make photoelectric current zero.

Suppose, VS is required stopping potential, e is charge on electron then eVo = ½ m (vmax)2.

Now, Einstein equation can be rewritten as h (vvo) = ½ m (vmax)2 = eVo.

From above equation we can easily observe that,

Stopping potential is directly proportional to the frequency of incident light and inversely proportional to work function.

Stopping potential is independent of

• Intensity of incident light

• Distance of the source from metal surface

• Illuminating power of the source

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Photoelectric Cell

A photocell is a technological application of the photoelectric effect. It is a device whose electrical properties are affected by light. It is also sometimes called an electric eye. Photocells are used in the reproduction of sound in motion pictures and in the television camera for scanning and telecasting scenes. They are used in industries for detecting minor flaws or holes in metal sheets.

Wave Nature of Matter

The wave nature of light shows up in the phenomena of interference, diffraction and polarisation. On the other hand, in photoelectric effect and Compton effect which involve energy and momentum transfer, radiation behaves as if it is made up of a bunch of particles – the photons.

A natural question arises: If radiation has a dual (wave-particle) nature, might not the particles of nature (the electrons, protons, etc.) also exhibit wave-like character?

de Broglie hypothesis attributes a wave like character to matter. If radiation shows dual aspects, so should matter.

De Broglie proposed that the wave length λ associated with a particle of momentum p is given by, λ = h/p = h/(m v), where m is the mass of the particle and v its speed.

The above equation is known as the de Broglie relation and the wavelength λ of the matter wave is called de Broglie wavelength.

The above equation shows that λ is smaller for a heavier particle (large m) or more energetic particle (large v).

Davisson’s and Germer’s Experiment

The experiment by Davisson’s and Germer’s provides experimental proof of the concept of wave nature of material particles.

The experimental arrangement used by Davisson and Germer is schematically shown in figure given below: In the experiment, an electron gun was used to produce a beam of electrons. This fine beam of accelerated electrons was made to fall on a nickel crystal and atoms of the crystal scatter these electrons in different directions. The intensity of electrons beam scattered in a given direction was observed by a detector. This detector was made to rotate on a circular scale. From the experiment, scientists observed the intensity of scattered beam of electrons for different values of latitude angles or scattering angles which are the angles between the incident and the scattered electron beams.

The experiment was performed by varying the accelerating voltage from 44 V to 68 V. It was noticed that a strong peak appeared in the intensity (I ) of the scattered electron for an accelerating voltage of 54V at a scattering angle θ = 50º.

The appearance of the peak in a particular direction is due to the constructive interference of electrons scattered from different layers of the regularly spaced atoms of the crystals. From the electron diffraction measurements, the wavelength of matter waves was found to be 0.165 nm.

CBSE Class 12th Physics Notes: Dual Nature of Radiation and Matter (Part ‒ I)