# Dual Nature of Radiation and Matter Class 12 | Physics | Term 2 |

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Dual Nature of Radiation and Matter Class 12 Notes, Physics, Term 2

Electron : It is an elementary particle having a negative charge of  1.60217662 × 10-19 coulombs and mass 9.10938356 × 10-31 kilograms

Photoelectric Effect : The phenomenon of emission of photoelectron from the surface of metal, when a light beam of suitable frequency is incident on it, is called photoelectric effect. The emitted electrons are called photoelectrons and the current so produced is called photoelectric current.

Hertz’ Observation : The phenomenon of photo electric emission was discovered in 1887 by Heinrich Hertz during his electromagnetic wave experiment. In his experimental investigation on the production of electromagnetic waves by means of spark across the detector loop were enhanced when the emitter plate was illuminated by ultraviolet light from an arc lamp.

Lenard’s Observation : Lenard observed that when ultraviolet radiation were allowed to fall on emitter plate of an evacuated glass tube enclosing two electrodes, current flows. As soon as, the ultraviolet radiations were stopped, the current flows also stopped. These observations indicate that when ultraviolet radiations fall on the emitter plate, electrons are ejected from it which are attracted towards the positive plate by the electric field.

#### Terms Related to Photoelectric Effects

(i) Free Electrons In metals, the electrons in the outer shells (valence electrons) are loosely bound to the atoms, hence they are free to move easily within the metal surface but cannot leave the metal surface. Such electrons are called free electrons.
(ii) Electron Emission The phenomenon of emission of electrons from the surface of a metal is called electron emission.
(iii) Photoelectric Emission It is the phenomenon of emission of electrons from the surface of metal when light radiations of suitable frequency fall on it.
(iv) Work Function The minimum amount of energy required to just eject an electron from the outer most surface of metal is known as work function of the metal. (v) Cut-off Potential For a particular frequency of incident radiation, the minimum negative (retarding) potential V0 given to plate for which the photoelectric current becomes zero, is called cut-off or stopping potential. (vi) Cut-off Frequency The minimum frequency of light which can emit photoelectrons from a material is called threshold frequency or cut-off frequency of that material.
(vii) Cut-off Wavelength The maximum wavelength of light which can emit photoelectrons from a material is called threshold wavelength or cut-off wavelength of that material.

#### Types of Electron Emission

• Thermionic Emission: In this type, the metal is heated to a sufficient temperature to enable the free electrons to come out of its surface.
• Field Emission: In this type, a very strong electric field is applied to the metal which pulls the electrons out of the surface due to the attraction of the positive field.
• Photoelectric Emission: In this type, the light of a certain frequency is made to fall on the metal surface which leads to the emission of electrons.

The current produced due to emitted electrons is called photocurrent.

Value of photoelectric current depends upon –

• The intensity of light
• The potential difference applied between the two electrodes
• The nature of the cathode material

Cut-off Potential For a particular frequency of incident radiation, the minimum negative (retarding) potential V0 given to plate for which the photoelectric current becomes zero, is called cut-off or stopping potential. Effect of Intensity of Light on Photo current For a fixed frequency of incident radiation, the photoelectric current increases linearly with increase in intensity of incident light. Effect of Potential on Photoelectric Current For a fixed frequency and intensity of incident light, the photoelectric current increases with increase in the potential applied to the collector. When all the photoelectrons reach the plate A, current becomes maximum it is known as saturation current. Effect of Frequency of Incident Radiation on Stopping Potential We take radiations of different frequencies but of same intensity. For each radiation, we study the variation of photoelectric current against the potential difference between the plates. Laws of Photoelectric Emission

(i) For a given material and a given frequency of incident radiation, the photoelectric current number of photoelectrons ejected per second is directly proportional to the intensity of the incident light.
(ii) For a given material and frequency of incident radiation, saturation current is found to be proportional to the intensity of incident radiation, whereas the stopping potential is independent of its intensity.
(iii) For a given material, there exists a certain minimum frequency of the incident radiation below which no emissions of photoelectrons takes place. This frequency is called threshold frequency.
Above the threshold frequency, the maximum kinetic energy of the emitted photoelectron or equivalent stopping potential is independent of intensity of incident light but depends only upon the frequency (or wavelength) of the incident light.
(iv) The photoelectric emission is an instantaneous process. The time lag between the incidence of radiations and emission of photoelectron is very small, less than even 10-9 s.

#### The Failure of Wave Theory to Explain Photoelectric Effect

(a) The wave nature of light fails to explain the photoelectric effect; this is because of the following reasons:
1) According to the Wave Theory/ picture of light, the energy carried/ possessed by a beam of light is measured in terms of the intensity of that beam of light as greater intensity implies greater amplitude and hence, the beam is said to be carrying greater energy. When a beam of light occurs on the metal, the energy possessed by the beam will be equally distributed among the electrons and these electrons on accepting energy will get ejected from the metal surface. When the waves of light of higher intensity fall on the metal surface, more energy will be imparted to the electrons. Hence, the kinetic energy of the emitted/ ejected electrons increases.
This was contradictory to the fact that: The maximum kinetic energy of the emitted electron is actually independent of the intensity of the incident beam of light.

2) According to the Wave Picture of Light, the energy possessed by the beam of light is smoothly and uniformly distributed across its advancing wavefronts. Thus, when the beam of light is incident on the metal surface, the energy carried by the beam is not received by just one electron. Instead, the energy is equally distributed among all the electrons that fall in the part of the surface of the metal which is illuminated. Thus, all the electrons receive this amount of energy distributed among them. Thus, each electron receives only a negligible amount of energy. So, the electron should take a finite amount of time to escape the surface of the metal.
This was contradictory to the fact that: The emission of photo – electrons takes place almost instantly or immediately after the light incidents on the metal surface.

(b) The phenomena of interference, diffraction and polarisation were explained by the wave picture of light. But the experimental study of the photoelectric effect cannot be explained with the help of the wave Picture of light. The wave picture was not able to explain the most basic features of photoelectric emission. So, a new theory was proposed to explain the phenomenon of photoelectric effect that is the Photon Picture of light. Photon is a packet or quanta of energy associated with electromagnetic radiation. The energy of a photon is given by E=hv , where,v is frequency associated with photon and h is Planck’s constant.

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

Einstein Photoelectric Equation : Energy Quantum of Radiation, Kmax = hv – Ф0 where, hv = energy of photon and Ф = work-function

NOTE: According to Planck’s quantum theory, light radiations consist of tiny packets of energy called quanta. One quantum of light radiation is called a photon which travels with the speed of light.

8. Relation between Stopping Potential (V0) and Threshold Frequency (v0)  Important Graphs related to Photoelectric Effect This graph shows that the photoelectric current (I) is independent of frequency of the incident light till intensity remains constant. Intensity and stopping potential (V0) graph Photoelectric cell or in short photocell is an instrument that develops electricity when light shines on it. It is actually to be an electron tube with a photosensitive cathode, but nearly all modern photocells are made with two electrodes which are separated by light-sensitive semiconductor material.

Dual nature of radiation- Light has dual nature .It manifests itself as a wave in diffraction , interference, polarisation etc. while it shows particle nature in photoelectric effect, compton scattering etc.

#### Davisson and Germer Experiment

• Davisson and Germer experiment showed the wave nature of electron for the first time
• They studied the diffraction effects of electron in crystal diffraction experiment
• The experimental setup for the experiment is shown below: The experimental setup consists of:

• Evacuated chamber for the free movement of electron without any air resistance
• Electron gun for the emission of electron
• Battery Used for the acceleration of electrons inside the cylinder
• Cylinder with fine hole along its axis connected to the battery so that electrons entering it could be accelerated to high speed
• Nickel  Target used to deflect electron beam towards the detector
• Movable detector(collector)to detect the intensity and scattering of electrons deflected by the nickel crystal at varying voltage supplies(44 to 68 V)
• Galvanometer to measure the small values of current

#### Observations

• Strong peak was detected at 55V, and the angle of scattering was observed to be 50°
• The pattern of deflected electrons was quite similar to the diffraction pattern of waves
• The wavelength corresponding to the electron (matter wave) was found to be λ = 0.165nm
• The experiment was in strong agreement with De Broglie’s hypothesis

According to De Broglie’s hypothesis, matter wave is given by: • The experiment proved that electrons behave as a wave under specific conditions as the scattering of electron gave rise to the diffraction pattern

On putting the value of V= 55V (the value at which a strong peak was detected), we get The wavelength calculated above using De Broglie’s hypothesis is equal to the wavelength observed in the Davisson and Germer experiment. So, Davisson and Germer experiment was consistent with De Broglie’s hypothesis.

• Hence, this experiment proved that electron behaves as a wave under specific conditions.

#### HEISENBERG’S UNCERTAINTY PRINCIPLE:

• This principle was in favor of the wave nature of matter
• It stated that it is impossible to simultaneously evaluate the precise position and momentum of particle. There is always some probability in predicting the position and momentum of a particle. Mathematically, it can be written as:

(Δx)(Δp) ≥ h/(2π)

Considering the above equation, 2 cases are possible:

• Case-1– If precise momentum(p) of an electron is known, then its wavelength by De Broglie’s hypothesis will be constant:

λ = h/p

It means that the wavelength has a fixed value and the wave is extended infinitely throughout the wave. Hence, it is impossible to find the position of the wave.

Mathematically, if  p = fixed  , Then, Δp→0, Δx→∞ • Case-2- If the wave is localized, having finite end points

A localized wave is shown below: As we can see in the diagram, the wavelength (λ) is not fixed, so the momentum (p) is also not fixed.

Hence, there is uncertainty in both, momentum (p) and position (x).

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 Dual Nature of Radiation and Matter

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