1. Quantum mechanics is a mathematical model that describes the behavior of the particles on an atomic and subatomic scale.
2. According to Planck's quantum theory, the Energy of light comes in form of packets (it is not a material particle). These packets are called Quanta or Photons.
3. Energy of the photon depends on frequency. Frequency does not change with changing medium. Energy is given by \[ E = hf = (6.636 \times 10^{-34})f\]
4. Energy of the photon having wavelength $ \lambda $ is given by \[ E = \frac{hc}{\lambda} = \frac{12400}{\lambda (\ in \ Angstrom)}eV \] and momentum of photon is given by \[ p = \frac{h}{\lambda} \] where $ h $ is plack's constant and $ c $ is speed of light.
5. Photons are electrically neutral particles. These are not deflected by the electric and magnetic fields.
6. Photons can collide with material particles like electrons. During the collision, total Energy and total momentum remain constant i.e. collision is elastic.
7. Rest mass of the photon is zero. This means that photon does not exist at rest. Equivalent mass of the photon is given by, \[ m = \frac{hf}{c^2} \]
8. Intensity is defined as energy radiated per unit time per unit area. i.e. \[ I = \frac{E}{tA}= \frac{P}{A} \] where P is power. SI unit of intensity is $ \frac{W}{m^2} $.
9. A source is at power P and emitting radiation energy of wavelength $ \lambda $ then number of photons emitted by the source per second is given by, \[ n = \frac{P}{E}= \frac{P \lambda}{hc} \]
10. Photon Flux is the number of photons incident on a surface normally per second per unit area. \[ Photon \ Flux, \phi = \frac{Intensity}{Energy \ of \ a \ photon} = \frac{I\lambda}{hc} \]
11. When radiation is incident on the surface then it will apply some force on the surface. If radiation falls on the surface at some angle and is reflected by the surface, the average force is given by, \[ F = \frac{2IAcos^2\theta}{c} \]Radiation pressure is given by, \[ P = \frac{2Icos^2\theta}{c} \]
Study of Photoelectric Effect
12. Minimum energy required to escape an electron from the surface is known as Work Function $ \phi $. The minimum frequency of incident light that is just capable of ejecting electrons from metal is called the threshold frequency.
Metal Work Function (eV)
Cesium 1.9
Potassium 2.2
Sodium 2.3
Lithium 2.5
Calcium 3.2
Copper 4.5
Silver 4.7
Platinum 5.6
13. When electromagnetic radiation of suitable wavelength is incident on the metal surface such that electrons emitted from the surface, this phenomenon is known as Photoelectric emission.
14. When energy is given in form of heat to the metal surface such that electrons are emitted from the surface, this phenomenon is known as Thermionic emission.
15. When the strong field is applied in such a way that electrons get accelerated and overcome the potential barrier, this phenomenon is known as Field emission.
16. The phenomenon of the photoelectric effect was discovered by Heinrich Hertz in 1887. While performing an experiment for the 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 were directed at one of the metal plates. Hertz could not explain his observations.
17. 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, the electrons are ejected from it, which are attracted towards the anode plate. The electrons flow through the evacuated glass tube, complete the circuit and current begins to flow in the circuit.
18. Hallwachs studied further by taking a 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 a 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.
19. Einstein's Photoelectric equation is \[ hf = \phi + KE \implies \frac{1}{2}mv^2 = hf - \phi \]where f is incident frequency and v is maximum velocity of the electron.
20. Photoelectric current is directly proportional to the intensity of the incident light keeping frequency and potential the same. On increasing the intensity, photoelectric current will increase and vice-versa. It does not depend on the incident energy.
21. If the collector is given negative potential with respect to the emitter, then at some potential electrons will not reach the collector. Due to this, there will be no current in the circuit. If the potential of the collector is further increased in the negative, no current will be in the circuit. This potential at which the photoelectric current is zero is known as Stopping Potential. \[ eV_0 = K.E. = \frac{1}{2}mv^2 \]Stopping potential is independent of the intensity of the incident light. It depends only on the incident energy.
22. Kinetic energy of the electrons depends only on the incident energy, not on the intensity of the incident light.
23. There is no time lag between the incidence of light and the emission of photoelectrons.
24. De Broglie gave the wavelength associated with moving object, which is given by, \[ \lambda = \frac{h}{mv} = \frac{h}{p} \]where m is mass of the object and v is the speed of the object.
25. If E is the kinetic energy of the electron, then the De-Broglie wavelength of the electron will be \[ \lambda = \frac{h}{\sqrt{2mE}} \]
26. If electron is accelerated by potential V then De-Broglie wavelength of electron will be \[ \lambda = \frac{h}{\sqrt{2meV}} \]
27. Davisson and Germer Experiment gives the experimental evidence for the wave nature of the electrons.
