1. Dual Nature of Radiations
It is well known that the phenomena of interference, diffraction and polarisation indicate that light has wave nature. But some phenomena like Photoelectric effect, Compton effect, Emission and Absorption of radiation could not be explained by wave nature.
These were explained by particle (quantum) nature of light. Thus, light (radiation) has dual nature.
2. Quantum Nature of Light: Concept of a Photon
Some phenomena like Photoelectric effect, Compton effect, Raman effect could not be explained by wave theory of light. Therefore, quantum theory of light was proposed by Einstein. According to quantum theory of light “light is propagated in bundles of small energy, each bundle being called a photon and possessing energy.”
where ν is frequency, λ is wavelength of light and h is Planck’s constant = 6.62 × 10–34 joule second and c = speed of light in vacuum = 3 × 108 m/s.
Momentum of photon,
Rest mass of photon = 0
Dynamic or kinetic mass of photon,
3. Photoelectric Effect
The phenomenon of emission of electrons from a metallic surface by the use of light (or radiant) energy is called photoelectric effect. The phenomenon was discovered by Lenard. For photoelectric emission, the metal used must have low work function, e.g., alkali metals. Caesium is the best metal for photoelectric effect.
4. Hertz’s Observations
The phenomenon of photoelectric effect was discovered by Heinrich Hertz in 1887. While performing an experiment for production of electromagnetic waves by means of spark discharge, Hertz observed that sparks occurred more rapidly in the air gap of his transmitter when ultraviolet radiations was directed at one of the metal plates. Hertz could not explain his observations.
5. Lenard’s Observations
Phillip Lenard observed that when ultraviolet radiations were made incident on the emitter plate of an evacuated glass tube enclosing two metal plates (called electrodes), current flows in the circuit, but as soon as ultraviolet radiation falling on the emitter plate was stopped, the current flow stopped. These observations indicate that when ultraviolet radiations fall on the emitter (cathode) plate C, the electrons are ejected from it, which are attracted towards anode plate A. The electrons flow through the evacuated glass tube, complete the circuit and current begins to flow in the circuit.
Hallwachs Exp.: Hallwachs studied further by taking a zinc plate and an electroscope. The zinc plate was connected to an electroscope. He observed that:
(i) When an uncharged zinc plate was irradiated by ultraviolet light, the zinc plate acquired positive charge.
(ii) When a positively charged zinc plate is illuminated by ultraviolet light, the positive charge of the plate was increased.
(iii) When a negatively charged zinc plate was irradiated by ultraviolet light, the zinc plate lost its charge.
All these observations show that when ultraviolet light falls on zinc plate, the negatively charged particles (electrons) are emitted.
Further study done by Hallwach’s experiment shows that different metals emit electrons by different electromagnetic radiations. For example the alkali metals (e.g., sodium, caesium, potassium etc.) emit electrons when visible light is incident on them. The heavy metals (such as zinc, cadmium, magnesium etc.) emit electrons when ultraviolet radiation is incident on them.
Caesium is the most sensitive metal for photoelectric emission. It can emit electrons with less-energetic infrared radiation.
In photoelectric effect the light energy is converted into electrical energy.
6. Characteristics of Photoelectric Effect
(i) Effect of Intensity: Intensity of light means the energy incident per unit area per second. For a given frequency, if intensity of incident light is increased, the photoelectric current increases and with decrease of intensity, the photoelectric current decreases; but the stopping potential remains the same.
Intensity of radiations can be increased/decreased by varying the distance between source and metal plate (or emitter).
This means that the intensity of incident light affects the photoelectric current but the maximum kinetic energy of photoelectrons remains unchanged as shown in fig (b).
(ii) Effect of Frequency: When the intensity of incident light is kept fixed and frequency is increased, the photoelectric current remains the same; but the stopping potential increases.
If the frequency is decreased, the stopping potential decreases and at a particular frequency of incident light, the stopping potential becomes zero. This value of frequency of incident light for which the stopping potential is zero is called threshold frequency ν0. If the frequency of incident light (ν) is less than the threshold frequency (ν0) no photoelectric emission takes place.
Thus, the increase of frequency increases the maximum kinetic energy of photoelectrons but the photoelectric current remain unchanged.
(iii) Effect of Photometal: When frequency and intensity of incident light are kept fixed and photometal is changed, we observe that stopping potential (VS) versus frequency (ν) graphs are parallel straight lines, cutting frequency axis at different points (Fig.). This shows that threshold frequencies are different for different metals, the slope (VS / ν) for all the metals is same and hence a universal constant.
(iv) Effect of Time: There is no time lag between the incidence of light and the emission of photoelectrons.
7. Some Definitions
Work Function: The minimum energy required to free an electron from its metallic bonding is called work function. It is denoted by W or
Threshold Frequency: The minimum frequency of incident light which is just capable of ejecting electrons from a metal is called the threshold frequency. It is denoted by ν0. It is different for different metal.
Stopping Potential: The minimum retarding potential applied to anode of a photoelectric tube which is just capable of stopping photoelectric current is called the stopping potential. It is denoted by V0 (or VS)
8. Einstein’s Explanation of Photoelectric Effect: Einstein’s Photoelectric Equation
Einstein extended Planck’s quantum idea for light to explain photoelectric effect.
The assumptions of Einstein’s theory are:
1. The photoelectric effect is the result of collision of a photon of incident light and an electron of photometal.
2. The electron of photometal is bound with the nucleus by coulomb attractive forces. The minimum energy required to free an electron from its bondage is called work function (W).
3. The incident photon interacts with a single electron and loses its energy in two parts:
(i) in releasing the electron from its bondage, and
(ii) in imparting kinetic energy to emitted electron.
Accordingly, if hν is the energy of incident photon, then from law of conservation of energy
or maximum kinetic energy of photoelectrons,
where W is work function. This equation is referred as Einstein’s photoelectric equation and explains all experimental results of photoelectric effect. If Vs is stopping potential, then
Stopping potential,
The slope of Ek versus ν graph is h.
The slope of VS versus ν graph is
9. Photocell
A photocell is a device which converts light energy into electrical energy. It is also called electric eye.
10. Matter Waves: Wave Nature of Particles
Light exhibits particle aspects in certain phenomena (e.g., photoelectric effect, emission and absorption of radiation), while wave aspects in other phenomena (e.g., interference, diffraction and polarisation). That is, light has dual nature. In analogy with dual nature of light, de Broglie thought in terms of dual nature of matter.
11. de Broglie Hypothesis
Louis de Broglie postulated that the material particles (e.g., electrons, protons, α-particles, atoms, etc.) may exhibit wave aspect. Accordingly, a moving material particle behaves as wave and the wavelength associated with material particle is
If Ek is kinetic energy of moving material particle, then
i.e.,
The wave associated with material particle is called the de-Broglie wave or matter wave. Thede-Broglie hypothesis has been confirmed by diffraction experiments.
For charged particles associated through a potential of V volt,
Ek = qV
For electrons, q = e =1.6 × 10–19 C, m = 9 ×10–31 kg
For electron orbiting in an atom, de Broglie wavelength is given as
For neutral particles in thermal equilibrium at absolute temperature T, Ek = kT
12. Davisson and Germer Experiment
This experiment gave the first experimental evidence for the wave nature of slow electrons. Later on, it was shown that all material particles in motion behave as waves.
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