CBSE Class 12 Chemistry Dual Nature of Radiation and Matter Exam Notes

CBSE Class 12 Chemistry Dual Nature of Radiation and Matter Exam Notes. Please refer to the examination notes which you can use for preparing and revising for exams. These notes will help you to revise the concepts quickly and get good marks.

Physics: Dual Nature of Radiation and Matter

1. ELECTRON EMISSION

1. Electron emission refers to the liberation of free electrons from the surface of a substance aided by the external energy transferred to the electrons.
2. It tends to occur on metals because metals are rich in free electrons.
3. The amount of external energy required to emit an electron from the metal surface is known as work function, which depends on the nature of the metal.
4. The work function is usually expressed in electron volt (eV) unit.

Methods for obtaining electron emission from the metal surface

1. Thermionic Emission: Filaments get heated while passing current through them and on sufficient heating electrons are emitted. Triodes, cathode ray tubes etc. are based on this principle.
2. Field Emission: In this process, free electrons are pulled out by applying strong electric fields of the order of \(10^{8}\ \text{V m}^{-1}\).
3. Photoelectric Emission: When electromagnetic radiation of sufficiently high frequency falls on a clean metal surface, free electrons are emitted from the surface. The electrons so emitted are called the photoelectrons.

2. PHOTOELECTRIC EFFECT

1. Hertz observed that if cathode is irradiated with ultraviolet radiations, spark of high voltage passes through the gap between the electrodes.
2. Lenard’s experiments lead to the discovery of a current between the electrodes assembled in an evacuated glass tube, when the emitter plate was illuminated using UV radiations. The current existed only when UV radiations were incident on the same.
3. Hallwachs further studied this and found that when negatively charged zinc plate with an electroscope is irradiated with ultraviolet light, negative charge on the plate decreased or vanished. If neutral plate were used, it became positive and a positive plate more positive. This lead to the conclusion that negatively charged particles were emitted from the plate.
4. Photoelectric effect refers to the phenomenon of emission of electrons from the surface of metals (like Zn, Cs, K etc.) when irradiated with high frequency electromagnetic radiations.
5. For emission of photoelectrons, the frequency of the incident light should be more than certain minimum called threshold frequency (\(\nu_0\)) whose value depends on the type of the metal.
6. For most of the metals, threshold frequency lies in ultraviolet band of electromagnetic spectrum. A few metal have the same in the visible region.

Experimental Study

The experimental arrangement to study photoelectric effect consists of an evacuated glass tube with cathode C and anode A near either ends. UV rays from the source S fall on C and electrons are emitted. A circuit can be created so that the photoelectrons initiate a current. The potential of electrode A can be adjusted with reference to the electrode C. The following observations have been made.

1. The photoelectric current is directly proportional to the intensity of light. When the frequency of incident radiation and the accelerating potential remain the same, the number of photoelectrons emitted per second is directly proportional to the intensity of the incident radiation.

2. The strength of photoelectric current increases with the increase in accelerating potential, but only upto a saturation value.

If a negative (retarding) potential is given to anode, the electrons get repelled and as a result the photoelectric current decreases. With the increase in retarding potential of the anode, the photoelectric current rapidly decreases and becomes zero at a particular value of retarding potential called stopping potential (\(V_0\)).

1. Photoelectric current becomes zero when the retarding potential is sufficient to repel the electrons with maximum kinetic energy. \(KE_{max}=eV_0\)
2. For a given frequency of radiation, the value of stopping potential is independent of the intensity of radiation.

3. Stopping potential depends on the frequency of the incident radiation and the nature of the metal.
4. For a given metal, the value of stopping potential becomes more negative as the frequency of the incident radiation increases (\(\nu_3>\nu_2>\nu_1\)).

5. Different metals have different values of stopping potential for the same frequency of radiations.

6. There is a certain minimum cut-off frequency for each metal for which the stopping potential is zero. This cut-off frequency is referred to as threshold frequency.
7. The photoelectric emission is an instantaneous process without any apparent time lag (\(<10^{-9}\ \text{s}\) or less), even when the intensity of incident radiation is very less.

3. EINSTEIN’S PHOTOELECTRIC EQUATION

1. Failure of wave theory:
   1. According to wave theory, more intense light supplies more energy and so the kinetic energy of photoelectrons should increase with the intensity of light. But experiments show that the maximum kinetic energy of photoelectrons is independent of the intensity of light.
   2. According to wave theory, the photoelectric effect should take place irrespective of the frequency of light, provided the intensity is sufficient to supply required energy to the electrons. But experiments confirm a threshold frequency, below which no emission of electrons takes place.
   3. If wave theory were correct, the electrons would take some time to absorb sufficient energy and leave the metal surface, i.e. there is a time delay between the irradiation of the surface and the emission of electrons. However, no such time delay was detected.
2. Einstein modified quantum theory of light and explained photoelectric effect on the basis of that.
   1. In photoelectric effect, light behaves as particles called photons.
   2. Photon is a discrete unit (quantum) of light energy with no charge and zero rest mass.
   3. Photon can transfer energy (\(E=h\nu\)) and momentum \(p=\dfrac{E}{c}\).
   4. When a photon undergoes a direct inelastic collision with an electron, the energy of photon (\(E=h\nu\)) is completely absorbed. This makes the electron more energetic.
   5. If the energy absorbed by an electron at the surface is higher than the work function (\(\phi\)), then the emission of electron takes place.
   6. A part of the energy absorbed by an electron at the surface is utilised towards the work function and the rest appears as the maximum kinetic energy (\(KE_{max}\)) of the electron.
3. Therefore,\[h\nu=\phi+KE_{max}\qquad\text{or,}\qquad KE_{max}=h\nu-\phi\quad\ldots(i)\]Equation (i) is referred to as Einstein’s photoelectric equation.
4. If the energy transferred by the photon is just sufficient to eject the electron from the surface, then the frequency of photon is threshold frequency \(\nu_0\). Here, KE = 0 and\[h\nu_0=\phi\quad\ldots(ii)\]
5. From (i) and (ii), Einstein’s photoelectric equation becomes,\[KE_{max}=h(\nu-\nu_0)\]
6. Success of Einstein’s explanation:
   1. Photoelectric current depends on the number of electrons emitted per second. But this is directly proportional to the number of photons incident which in turn increases with the intensity of light. Therefore, photoelectric current increases with the intensity of light. (This is when \(\nu\) is a constant)
   2. Photoelectric equation shows that the maximum kinetic energy varies linearly with the frequency of the incident radiation and is independent of intensity.
   3. Photoelectric equation also shows that when \(\nu<\nu_0\), kinetic energy is negative. This is impossible. It necessitates the frequency of radiation to be equal to or greater than the threshold frequency.
   4. The energy of photon is localised and the electron is knocked out as soon as the photon with sufficient energy meets the electron. There is no detectable time lag in this process.
   5. The plot between \(KE_{max}\) and \(\nu\) is a straight line, the slope of which gives the value of the Planck’s constant (h). This verifies Einstein’s theory experimentally.

4. PARTICLE NATURE OF LIGHT - PHOTON

The particle nature of light is revealed in photoelectric effect. Light photon interacted with electron as a quantum of energy. The reverse can be seen in Compton effect, where, the X-ray photons get scattered by electrons as if they are real particles.

The properties of photons can be summarised as follows.

1. Photons have no charge and zero rest mass.
2. They can be considered a real particle having mass \(m=\dfrac{h\nu}{c^{2}}\) (as \(E=mc^2\)).
3. The energy associated with a photon of frequency \(\nu\) is \(h\nu\).
4. Einstein has defined the relation between energy (E) and momentum (p) of a particle in special theory of relativity as\[E=\sqrt{p^{2}c^{2}+m_0^{2}c^{4}}\]where, \(m_0\) is the rest mass of the particle. This is applicable to photons as well. If the rest mass of the particle is zero, \(E=pc\).
5. ∴ Momentum of photon of frequency \(\nu\) is \(p=\dfrac{E}{c}=\dfrac{h\nu}{c}\).
6. Photon, like a real particle, interacts with other particles following the laws of conservation of momentum and energy.

5. WAVE NATURE OF MATTER

1. Photoelectric effect and Compton effect can be explained by using the particle nature of light.
2. Momentum (p) of a photon of wavelength (\(\lambda\)) is given by: \(p=\dfrac{h}{\lambda}\).
3. Certain experiments revealed that electrons produced patterns attributed to waves. It lead to the conclusion that electron had wavelike properties.
4. Louis de Broglie established a relation between the momentum and wavelength of an electron that can be given as:\[\text{Wavelength}=\frac{\text{Planck’s constant}}{\text{Momentum}}\]\[\lambda=\frac{h}{p}=\frac{h}{mv}\qquad\ldots(i)\]Equation (i) is called de Broglie relation and \(\lambda\) is the wavelength of matter wave called de Broglie wavelength.
5. de Broglie equation is applicable to all types of matter. It shows that \(\lambda\) is smaller for heavier particles.
6. In certain situations like electron diffraction, it is easier to measure the kinetic energy (K) of the electron than its momentum.\[K=\frac12mv^{2}\ \Rightarrow\ mv=\sqrt{2mK}\]Equation (i) becomes, \[\lambda=\frac{h}{\sqrt{2mK}}\qquad\ldots(ii)\]
7. For an electron accelerated from rest through a potential difference of V volts, K = eV. Then (ii) becomes,\[\lambda=\frac{h}{\sqrt{2meV}}\qquad\ldots(iii)\]
8. Putting the values of h, m and e in (iii),\[\lambda=\frac{1.227}{\sqrt V}\ \text{nm}\]
9. Matter waves associated with electrons could be verified by crystal diffraction experiments.
10. Equation (iii) can be generalised for any charged particle with mass m and charge q accelerated through a pd of V volts:\[\lambda=\frac{h}{\sqrt{2mqV}}\]
11. A concept of wave packet is introduced to explain the wave activity of matter waves. The figure shows the resultant of the superposition of many harmonic waves with continuously changing wavelengths. The non-zero displacement of the resulting wave limited to a small part of the space can represent a particle.

12. The concept of matter waves led to Heisenberg’s uncertainty principle. The probability of finding a particle is greater in the region of its greater displacement. For a single harmonic wave, such a probability is the same anywhere on its path or, the position of the particle is uncertain. But the wavelength of the single harmonic wave is definite, so its momentum (\(p=\dfrac{h}{\lambda}\)) is also definite. If more waves are superposed and the wave packet is made finite, the position of the particle will be more definite. But in such a wave packet, the wavelength of the wave packet and hence its momentum becomes uncertain.
13. Heisenberg’s uncertainty principle states that it is not possible to measure both the position and momentum of an electron (or any other particle) at the same time exactly. If the uncertainty in the x-coordinate of the position of a particle is \(\Delta x\) and uncertainty in the x-component of its momentum is \(\Delta p\), then\[\Delta x\cdot\Delta p\approx\frac{h}{2\pi}=\hbar\qquad(\hbar\ \text{is defined to be}\ \tfrac{h}{2\pi})\]

    ⇒ if \(\Delta x\to0\), then \(\Delta p\to\infty\) and if \(\Delta p\to0\), then \(\Delta x\to\infty\).

    In general, \(\Delta x\) and \(\Delta p\) are non-zero and their product is of the order \(\hbar\).

6. DAVISSON - GERMER EXPERIMENT

In 1927, Davisson and Germer performed experiments to study scattering of electrons by a piece of nickel placed in vacuum. The experimental set up is shown in the figure below.

G is an electron gun having tungsten filament coated with barium oxide. The electrons emitted by the filament are accelerated using high voltage (V). The electrons are made into a thin beam by a cylinder. The electron beam is made incident on a piece of nickel (C) and get scattered by the atoms of Nickel. D is a detector which can be moved in an arc. The electrons scattered in different directions are detected by D. The current through the detector is measured by the galvanometer which indicates the number of electrons scattered in that direction.

The variation of the intensity (I) of the scattered electrons with the angle of scattering \(\theta\) is obtained for different accelerating voltages. 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 54 V at a scattering angle \(\phi=50^\circ\).

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.

V, m and e representing the accelerating voltage, mass and charge of the electron respectively, the wavelength is given by,\[\lambda=\frac{h}{\sqrt{2meV}}\]

Putting V = 54 V, \(h=6.62\times10^{-34}\ \text{J s}\), \(m=9.1\times10^{-31}\ \text{kg}\) and \(e=1.6\times10^{-19}\ \text{C}\), the value of \(\lambda\) works out to be \(1.66\times10^{-10}\ \text{m}\) or 0.166 nm.

Thus, it is found that the theoretical value for the de Broglie wavelength is in agreement with the value obtained by Davisson–Germer experiment. This confirms the wave nature of electrons and the de Broglie relation.