Class 12 Physics Notes Chapter 3 (Dual Nature of Radiation and Matter) – Physics Part-II Book

Detailed Notes with MCQs of Chapter 3: Dual Nature of Radiation and Matter from your Physics Part-II book. This is a crucial chapter, bridging classical and modern physics, and frequently tested in government exams. Pay close attention to the concepts and formulas.

Chapter 3: Dual Nature of Radiation and Matter - Detailed Notes

1. Introduction:

• Classical physics described light purely as an electromagnetic wave (Maxwell's theory) and matter purely as particles (Newtonian mechanics).
• However, phenomena like the photoelectric effect, Compton scattering, blackbody radiation couldn't be explained by the wave nature of light alone. Similarly, electron diffraction showed wave-like behaviour of particles.
• This led to the concept of dual nature: Radiation (like light) and matter (like electrons) can exhibit both wave and particle properties depending on the experiment or phenomenon being observed.

2. Electron Emission:

• The phenomenon of liberation of electrons from a metal surface. Requires external energy.
• Types:
  • Thermionic Emission: Heating the metal provides thermal energy to electrons.
  • Field Emission: Applying a very strong electric field (~10⁸ V/m) pulls electrons out.
  • Photoelectric Emission: Shining light (electromagnetic radiation) of suitable frequency provides energy to electrons. (This is the focus of the chapter).

3. Photoelectric Effect:

• Definition: The phenomenon of emission of electrons from a metal surface when electromagnetic radiation of sufficiently high frequency falls on it. The emitted electrons are called photoelectrons, and the resulting current is the photocurrent.

• Experimental Setup (Hertz, Hallwachs, Lenard's observations): Typically involves an evacuated glass tube with an emitter plate (cathode) and a collector plate (anode), connected to a variable voltage source and an ammeter/galvanometer.

• Key Experimental Observations & Laws of Photoelectric Emission:

  1. Threshold Frequency (ν₀): For a given metal, there exists a minimum frequency of incident radiation below which no photoelectric emission occurs, however high the intensity. This is the threshold frequency. Corresponding wavelength is threshold wavelength (λ₀), where λ₀ = c/ν₀.
  2. Instantaneous Process: Photoelectric emission is an almost instantaneous process (time lag < 10⁻⁹ s) as soon as radiation of suitable frequency hits the surface.
  3. Intensity Dependence: For a frequency ν > ν₀, the photoelectric current (number of photoelectrons emitted per second) is directly proportional to the intensity of the incident radiation.
  4. Frequency Dependence (Kinetic Energy): For a frequency ν > ν₀, the maximum kinetic energy (KE_max) of the emitted photoelectrons is independent of the intensity but depends linearly on the frequency of the incident radiation. KE_max increases as frequency increases.
  5. Stopping Potential (V₀): There exists a minimum negative (retarding) potential applied to the anode for which the photocurrent becomes zero. This is the stopping potential. At this potential, even the most energetic electron is repelled back.
     • KE_max = e V₀ (where 'e' is the electron charge)

• Failure of Classical Wave Theory:

  • Existence of Threshold Frequency: Wave theory predicts emission should occur for any frequency if intensity is high enough (energy accumulates). This contradicts observation 1.
  • Instantaneous Emission: Wave theory suggests electrons need time to absorb enough energy from the wavefront. This contradicts observation 2.
  • KE dependence on Frequency, not Intensity: Wave theory links energy to intensity (amplitude squared), predicting KE_max should depend on intensity, not frequency. This contradicts observation 4.

4. Einstein's Photoelectric Equation (1905):

• Based on Planck's Quantum Theory (E = hν), Einstein proposed that light consists of discrete packets of energy called photons.
• Photon Energy: E = hν = hc/λ (where h = Planck's constant ≈ 6.63 × 10⁻³⁴ J s, ν = frequency, c = speed of light, λ = wavelength).
• Explanation: When a photon of energy hν strikes the metal surface, its energy is used in two ways:
  1. A part overcomes the surface barrier to liberate the electron (Work Function, Φ₀).
  2. The remaining energy appears as the maximum kinetic energy (KE_max) of the emitted electron.
• Energy Conservation:
  Incident Photon Energy = Work Function + Maximum Kinetic Energy of Electron
  hν = Φ₀ + KE_max
• Work Function (Φ₀): The minimum energy required to just eject an electron from the metal surface. It's characteristic of the metal. Φ₀ = hν₀ = hc/λ₀.
• Forms of the Equation:
  • hν = hν₀ + KE_max
  • KE_max = hν - hν₀ = h(ν - ν₀)
  • Since KE_max = ½ mv_max² = eV₀:
    • eV₀ = hν - Φ₀
    • V₀ = (h/e)ν - (Φ₀/e)
• Graphical Interpretations:
  • KE_max vs ν (or V₀ vs ν): A straight line with slope h (or h/e) and y-intercept -Φ₀ (or -Φ₀/e). The x-intercept gives the threshold frequency ν₀.
  • Photocurrent vs Intensity: A straight line passing through the origin (for ν > ν₀).
  • Photocurrent vs Anode Potential: Current increases initially, then saturates. Increasing intensity increases saturation current but not stopping potential. Increasing frequency increases stopping potential (and KE_max) but not saturation current.

5. Particle Nature of Light: The Photon

• Properties of Photons:
  • Travel at the speed of light (c) in vacuum.
  • Have zero rest mass.
  • Carry energy E = hν = hc/λ.
  • Carry momentum p = E/c = hν/c = h/λ.
  • Are electrically neutral.
  • Are not deflected by electric or magnetic fields.
  • In a photon-particle collision (like photon-electron), total energy and total momentum are conserved. The number of photons may not be conserved (photon can be absorbed or created).

6. Wave Nature of Matter: de Broglie Hypothesis (1924)

• Louis de Broglie proposed that matter, like radiation, should exhibit dual nature. Moving particles should have wave-like properties.
• de Broglie Wavelength (λ): The wavelength associated with a moving particle is given by:
  λ = h / p = h / mv
  (where p = momentum, m = mass, v = velocity of the particle).
• Significance: λ is inversely proportional to momentum (and mass).
  • For macroscopic objects (ball, car), mass is large, so λ is extremely small and undetectable.
  • For microscopic particles (electrons, protons, neutrons), mass is small, so λ can be significant and measurable (comparable to atomic spacing in crystals, allowing diffraction).
• de Broglie Wavelength of an Electron Accelerated by Potential V:
  • If an electron (charge e, mass m) is accelerated from rest through a potential difference V, its kinetic energy KE = eV.
  • KE = p²/2m => p = √(2m KE) = √(2meV)
  • λ = h / p = h / √(2meV)
  • Substituting values for h, m, e:
    λ ≈ 12.27 / √V Å (where V is in Volts)

7. Davisson-Germer Experiment (1927):

• Aim: To experimentally verify the wave nature of electrons.
• Setup: Electrons emitted from a heated filament are accelerated by a potential difference (V) and directed towards a Nickel crystal. A movable detector measures the intensity of scattered electrons at different angles.
• Observation: A strong peak in intensity was observed at a specific scattering angle (50°) for a particular accelerating voltage (54 V). This peak was interpreted as constructive interference of electron waves diffracted by the crystal lattice planes, similar to X-ray diffraction (Bragg's law).
• Conclusion: The calculated de Broglie wavelength for 54 V electrons (λ ≈ 1.67 Å) matched well with the wavelength determined from the diffraction pattern using Bragg's law (λ ≈ 1.65 Å). This confirmed the wave nature of electrons.

8. Heisenberg's Uncertainty Principle (Contextual Link):

• While often detailed later, it's fundamentally linked to duality. It states that it's impossible to simultaneously measure both the position (Δx) and momentum (Δp) of a particle with absolute accuracy.
• Δx * Δp ≥ ħ/2 (where ħ = h/2π)
• This intrinsic uncertainty arises from the wave-particle duality – precisely defining position requires a localized wave packet (many wavelengths superimposed), which makes momentum uncertain, and vice versa.

Key Formulas Summary:

• Photon Energy: E = hν = hc/λ
• Photon Momentum: p = h/λ = E/c
• Work Function: Φ₀ = hν₀ = hc/λ₀
• Einstein's Photoelectric Equation: hν = Φ₀ + KE_max = hν₀ + eV₀
• Stopping Potential: V₀ = (h/e)ν - (Φ₀/e)
• de Broglie Wavelength (General): λ = h/p = h/mv
• de Broglie Wavelength (Electron, Potential V): λ = h/√(2meV) ≈ 12.27/√V Å

Multiple Choice Questions (MCQs):

1. In the photoelectric effect, the kinetic energy of emitted electrons depends on:
   a) Intensity of incident light
   b) Frequency of incident light
   c) Speed of incident light
   d) Angle of incidence

2. The work function of a metal is Φ₀. Photoelectric emission occurs only if the frequency (ν) of incident light is:
   a) ν < Φ₀/h
   b) ν = Φ₀/h
   c) ν > Φ₀/h
   d) ν can be any value if intensity is high

3. If the intensity of incident radiation in a photoelectric experiment is doubled (keeping frequency constant and ν > ν₀), the stopping potential will:
   a) Be doubled
   b) Be halved
   c) Remain unchanged
   d) Become zero

4. The momentum of a photon of wavelength λ is:
   a) hλ
   b) hc/λ
   c) h/λ
   d) hλ/c

5. An electron is accelerated through a potential difference of 100 V. Its de Broglie wavelength is approximately:
   a) 1.23 Å
   b) 12.3 Å
   c) 0.123 Å
   d) 123 Å

6. The Davisson-Germer experiment confirmed:
   a) The particle nature of light
   b) The wave nature of electrons
   c) The existence of the electron charge
   d) Bohr's atomic model

7. Which of the following properties is NOT associated with a photon?
   a) Energy
   b) Momentum
   c) Rest Mass
   d) Frequency

8. In Einstein's photoelectric equation, hν = Φ₀ + KE_max, the term Φ₀ represents:
   a) Energy of the incident photon
   b) Kinetic energy of the electron inside the metal
   c) Minimum energy required to eject an electron from the metal
   d) Stopping potential energy

9. If the threshold wavelength (λ₀) for a metal is 600 nm, what is its threshold frequency (ν₀)? (c = 3 × 10⁸ m/s)
   a) 5 × 10¹⁴ Hz
   b) 2 × 10¹⁴ Hz
   c) 1.8 × 10²¹ Hz
   d) 5 × 10¹⁵ Hz

10. According to de Broglie, the wavelength associated with a particle is:
    a) Directly proportional to its mass
    b) Directly proportional to its velocity
    c) Inversely proportional to its momentum
    d) Independent of its momentum

Answers to MCQs:

1. b) Frequency of incident light
2. c) ν > Φ₀/h
3. c) Remain unchanged
4. c) h/λ
5. a) 1.23 Å (Using λ ≈ 12.27/√V Å, √100 = 10, so λ ≈ 12.27/10 ≈ 1.23 Å)
6. b) The wave nature of electrons
7. c) Rest Mass (Photon rest mass is zero)
8. c) Minimum energy required to eject an electron from the metal
9. a) 5 × 10¹⁴ Hz (ν₀ = c/λ₀ = (3 × 10⁸ m/s) / (600 × 10⁻⁹ m) = 0.005 × 10¹⁷ Hz = 5 × 10¹⁴ Hz)
10. c) Inversely proportional to its momentum

Make sure you understand the underlying concepts behind each point and formula. Practice numerical problems based on the photoelectric equation and de Broglie wavelength. This chapter forms the foundation for understanding quantum mechanics. Good luck with your preparation!