By going through these CBSE Class 12 Physics Notes Chapter 11 Dual Nature of Radiation and Matter, students can recall all the concepts quickly.

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

→ Radiation has dual nature i.e., it behaves both as a particle and a wave.

→ Energy greater than work function (Φ_{0} or ω) required for ejection of electrons from the metal surface can be supplied by heating or irradiating it by the light of frequency greater than threshold frequency or applying a strong electric field.

→ The stopping potential (V_{0}) depends on the frequency of incident light, nature of the material on the surface of the cathode.

→ V_{0} is directly related to the maximum kinetic energy (\(\frac{1}{2}\) mV^{2}_{max}) of the emitted electrons i.e., eV_{0} = E_{max} = \(\frac{1}{2}\) m V^{2}_{max}).

→ V_{0} is independent of the intensity of incident light for a given frequency.

→ Below the threshold frequency (v_{0}), no photoelectric emission takes place whatever may be its intensity.

→ Photoelectric emission is an instantaneous process.

→ The photoelectric current depends on the potential difference applied between the cathode and anode, the nature of the material of the cathode, and the intensity of incident light.

→ The photoelectric emission follows the law of conservation of energy.

→ Each photon absorbed ejects an electron from a metal surface. Einstein’s photoelectric equation is in accordance with the law of conservation of energy.

→ The dualism of matter is inherent in the de-Broglie relation which contains a wave concept (λ) and a particle concept (p).

→ The de-Broglie wavelength (λ) associated with a moving particle is related to its momentum (p) as

λ = \(\frac{h}{p}\)

→ The de-Broglie wavelength is independent of the charge and nature of the material particle.

→ The wave nature of electrons has been verified and confirmed using Davisson and Germer’s experiments.

→ Free electrons in a metal are free in the sense that they move inside the metal in a constant potential.

→ Plank’s constant is the bridge between the particle aspect and wave aspect of radiation and matter.

→ The wave-particle duality is not the sole monopoly of e.m. waves.

→ Even a material particle in motion according to de-Broglie will have a wavelength.

→ The photoelectric effect was discovered by Hertz in 1887.

→ The photoelectric effect was demonstrated by Hallwach in 1888.

→ Work function is least for Caesium (i.e Φ_{0} = 2.14 eV)

→ Absorption of energy takes place in discrete units of hv.

→ Platinum has the highest value of work function.

→ Zn, Cd, Mg, etc. respond only to UV light (having a short wavelength) to cause electron emission from the surface.

→ Alkali metals such as Li, Na, K, Caesium, and rubidium are sensitive even to visible light.

→ The number of photoelectrons emitted per second is directly proportional to the intensity of incident radiation.

→ Work function: It is defined as the minimum energy required by an electron to come out from a metal surface.

→ Photo electrons: The electrons ejected out of a metal surface under the action of light of a short wavelength are called photoelectrons.

→ Photoelectric effect: It is defined as the phenomenon of ejection of electrons from a metal surface when the light of very high frequency falls upon it.

→ Photon: It is a packet of energy.

→ Photoelectric cell: ft is a device that converts light energy into electrical energy.

→ Matter waves or de-Broglie waves: They are defined as the waves associated with every moving matter particle.

→ Cutoff potential or Retarding potential or stopping potential: It is defined as the minimum value of negative potential which has to be applied on the anode in a photocell so that the photoelectric current becomes zero. It is denoted by V_{0}.

→ Saturation Current: It is the maximum value of the photoelectric current.

**Important Formulae**

→ For a relativistic particle moving with a speed v comparable to the speed of light c, de-Broglie wavelength is given by

λ = \(\frac{h}{m v}\)

where m = \(\frac{m_{0}}{\sqrt{1-\frac{v^{2}}{c^{2}}}}\), m_{0} being the rest mass of the particle.

→ deBroglie wavelength of a particle is

λ = \(\frac{\mathrm{h}}{\mathrm{p}}=\frac{\mathrm{h}}{\mathrm{m} v}=\frac{\mathrm{h}}{\sqrt{2 \mathrm{mE}}}=\frac{\mathrm{h}}{\sqrt{2 \mathrm{meV}}}\)

where p = momentum of particle of mass m, its velocity = v

E = K.E. of particle.

V = accelerating potential difference applied (V).

→ For an electron,

λ = \(\frac{12.27}{\sqrt{V}}\) A°

where \(\frac{\mathrm{h}}{\sqrt{2 \mathrm{me}}}\) = 12.27 × 10^{-10} for an electron

→ Vertical deflection of electron due to \(\overrightarrow{\mathrm{E}}\) between its plates is

y = \(\frac{1}{2}\) at2 = \(\frac{1}{2}\) . \(\frac{\mathrm{e} \mathrm{E}}{\mathrm{m}} \cdot \frac{\mathrm{x}^{2}}{v^{2}}\)

→ Total deflection of the charge on the screen is

y_{0} = \(\frac{\mathrm{eEx}}{\mathrm{m} v^{2}}\left(1+\frac{\mathrm{x}}{2}\right)=\left(1+\frac{\mathrm{x}}{2}\right)\) tan θ

where l = distance of screen from the end of plates.

x = length of plates

tan θ = \(\frac{v_{\mathrm{y}}}{v_{x}}=\frac{y_{0}}{\left(l+\frac{x}{2}\right)}\)

→ Einstein’s photoelectric equation is

hv = hv_{0} + \(\frac{1}{2}\) m v^{2}_{max}

or

\(\frac{hv}{λ}\) = W + eV_{0}, where the symbols have their usual meanings.

→ At the threshold frequency v^ the emitted phtoelectrons will have no K.E.

∴ 0 = hv_{0} – ω

or

ω = hv_{0}.

→ At stopping potential, \(\frac{1}{2}\) m v2 max = eV_{0}.

→ Be v max = \(\frac{m v_{\max }^{2}}{r}\)

→ p = \(\frac{hv}{C}\) = momentum of a photon

→ Slope of V – ν curve = \(\frac{\mathrm{V}}{\mathrm{ν}}=\frac{\mathrm{h}}{\mathrm{e}}\)

→ Number of photons per sec per unit area = \(\frac{Φ}{E}\)

= \(\frac{\text { energy flux }}{\text { energy of photons per sec per unit area }}\)

= \(\frac{\text { Energy radiated/sec }}{\text { Energy of each photon }}=\frac{\mathrm{P}}{\mathrm{E}}\)