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

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 (Φ₀ 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 (V₀) depends on the frequency of incident light, nature of the material on the surface of the cathode.

→ V₀ is directly related to the maximum kinetic energy (\(\frac{1}{2}\) mV²_max) of the emitted electrons i.e., eV₀ = E_max = \(\frac{1}{2}\) m V²_max).

→ V₀ is independent of the intensity of incident light for a given frequency.

→ Below the threshold frequency (v₀), 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 Φ₀ = 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 V₀.

→ 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 = \(\frac{m_{0}}{\sqrt{1-\frac{v^{2}}{c^{2}}}}\), m₀ 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
y₀ = \(\frac{\mathrm{eEx}}{\mathrm{m} v^{2}}\left(1+\frac{\mathrm{x}}{2}\right)=\left(1+\frac{\mathrm{x}}{2}\right)\) 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 = hv₀ + \(\frac{1}{2}\) m v²_max
or
\(\frac{hv}{λ}\) = W + eV₀, where the symbols have their usual meanings.

→ At the threshold frequency v^ the emitted phtoelectrons will have no K.E.
∴ 0 = hv₀ – ω
or
ω = hv₀.

→ At stopping potential, \(\frac{1}{2}\) m v2 max = eV₀.

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

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