RBSE Class 12 Physics Notes Chapter 11 Dual Nature of Radiation and Matter

These comprehensive RBSE Class 12 Physics Notes Chapter 11 Dual Nature of Radiation and Matter will give a brief overview of all the concepts.

RBSE Class 12 Physics Chapter 11 Notes Dual Nature of Radiation and Matter

Electron Emission and Photo-Electric Effect:

• Phenomenon of emission of electrons from a metal surface is called electron emission. Some work has to he done to eject electrons from the metal surface.
• The minimum amount of energy required to eject a free electron from the surface of metal is called work function of metal.

This minimum energy can be supplied to the free electrons in the metal for their release from the metal surface by any one of the following physical processes :

• Thermoionic emission. It is the process of emission of electrons from a metal surface by supplying suitable amount of heat.
• Photoelectric emission. It is the process of emission of electrons from a metal when radiations of certain frequency are incident on it.
• Field emission or cold cathode emission. It is the process of emission of electrons from a metal when a strong electric field is applied outside the metal surface.
• Secondary emission. It is the' process of emission of electrons from a metal when fast moving electrons (called primary electrons) fall on the metal surface.

Photons are packets of energy which are emitted by a source of radiations and travel in straight lines with speed of light, and energy possessed by each photon is h v, when h is given by h = 6.63 × 10^-34Js and is called Planck’s constant and v is frequency of photon
So E = h v = \(\frac{h c}{\lambda}\) (c is velocity of light & c = vλ)

Photoelectric effect:
Photoelectric effect is the phenomenon of ejection of electrons from a metal surface when illuminated by electromagnetic radiations of suitable wavelength (or frequency).

• The emitted electrons are called photoelectrons and the current so produced is called photoelectric current.
• Threshold Frequency (v₀) is the minimum value of incident radiations below which photoelectric emission stops altogether.

Stopping Potential:
Stopping Potential is the minimum value of negative (retarding) potential applied between emitter and collector, for which no photoelectron reaches collector. This is also called cut off potential or critical potential. At stopping potential, photoelectric current is zero.

Intensity of incident light in photoelectric effect is directly proportional to the photoelectric current when the frequency of incident light is more than threshold frequency.

Laws of photoelectric emission

• For a given photosensitive material, there is a minimum frequency called threshold frequency below which there is no photoelectric emission.
• Above threshold frequency, the photoelectric current is directly proportional to the intensity of incident radiations.
• Threshold frequency is independent of intensity of incident radiations but depends upon the frequency of incident radiations.
• Photoelectric emission is an instantaneous process.

Einstein's photoelectric equation
\(\frac{1}{2} \)mv² = h(v - v₀)

Photo cell or photoelectric cell is a device for converting light energy into electric energy.
Types of photocells

• Photoemissive cell
• Photovoltaic cell
• Photoconductive cell

Applications of photocell

• In burglar alarm
• T.V. transmission
• Solar batteries
• For controlling traffic
• Counting machine
• Fire alarm
• Automatic switching of street light circuit.

De-Broglie Dualistic Hypothesis
Louis de-Broglie predicted that like electro¬magnetic radiation, metal also has dual characteristics.
Matter in motion be accompanied by waves called the de-Broglie wave of definite wavelength. His suggestion was based on two assumptions.

• In this universe, the whole energy is in the form of matter and electromagnetic radiation.
• Nature loves symmetry, as the radiations have got dual nature, matter should also possess dual nature.

Derivation of de-Broglie wavelength
For photon. Energy of photon, E = hv ...(i)
From Einstein’s mass-energy relation
E = mc² ...(ii)
From (i) & (ii)
mc² = hv
mc = \(\frac{h v}{c}=\frac{h v}{v \lambda}=\frac{h}{\lambda}\)
or λ = \(\frac{h}{m c}=\frac{h}{p}\)

Similarly, for a material particle of mass in moving with velocity v, the wave associated with the material particle
λ = \(\frac{h}{m v}=\frac{h}{p}\)
This is called de-Broglie wave equation for a material particle. And the associated wave is called de-Broglie wave or matter wave.

So we find that wavelength of de-Broglie wave is independent of charge of particle and inversely proportional to the mass and momentum of the body. And de-Broglie waves (or matter waves) are not electromagnetic waves.

Experimental determination of wave nature of electron
The first experimental proof of the wave nature of electron was proved by Davisson and Germer.
The wavelength associated with an electron is given by
λ = \(\frac{12.27}{\sqrt{\mathrm{V}}}\)Å
This proves the existence of de-Broglie waves for the slow moving electrons.