NCERT Solutions for Class 12 Physics Chapter 11 Dual Nature of Radiation and Matter
NCERT Solutions for Class 12 Physics Chapter 11 Dual Nature of Radiation and Matter provides in-depth explanations of electron emission, photoelectric effect experiments, Einstein's photoelectric equation, photon energy concepts, and de Broglie wave-particle duality relations.
Overview of Topics & Subtopics (Click to Jump)
1. Electron Emission & Photoelectric Effect
Short Note:
• Work Function (ϕ₀ or W): Minimum energy required to emit an electron from a metal surface (unit: eV, where 1 eV = 1.6 × 10⁻¹⁹ J).
• Types of Electron Emission: Thermionic emission, Field emission, Photoelectric emission, and Secondary emission.
• Photoelectric Effect: Emission of electrons from a metal surface when light of suitable frequency strikes it.
- Threshold Frequency (ν₀): Minimum frequency of incident radiation below which no photoelectron emission takes place regardless of intensity.
- Stopping Potential (V₀): Minimum retarding potential applied to anode that completely stops the photoelectric current (K_max = e V₀).
- Photoelectric current is directly proportional to light intensity, provided frequency ν > ν₀.
2. Einstein's Photoelectric Equation & Photon Theory
Short Note:
• Photon Concept: Light consists of discrete packets of energy called quanta or photons. Each photon carries energy E = h ν = h c / λ and momentum p = E / c = h / λ.
• Einstein's Photoelectric Equation:
K_max = h ν - ϕ₀ => e V₀ = h ν - h ν₀ = h (ν - ν₀)
• Key Inferences:
1. Emission is instantaneous (time lag < 10⁻⁹ s).
2. Maximum Kinetic Energy (K_max) depends linearly on incident frequency, independent of intensity.
3. Intensity determines the number of emitted photoelectrons per second, not their energy.
3. Wave Nature of Matter & De Broglie Wavelength
Short Note:
• de Broglie Hypothesis: Moving material particles exhibit wave-like characteristics. The wavelength associated with a particle of momentum p is called the de Broglie wavelength (λ).
λ = h / p = h / (m v) = h / √(2 m K)
• de Broglie Wavelength of Electron Accelerated by Potential V:
λ = h / √(2 m e V) = 1.227 / √V nm = 12.27 / √V Å
• Davisson and Germer Experiment: Experimentally verified the wave nature of electrons by observing diffraction peaks when an electron beam scattered off a Nickel crystal target.
Intext & Conceptual Questions
• (i) Work Function (ϕ₀): It is the minimum amount of energy required to remove an electron from the outermost surface of a metal without imparting any kinetic energy to it. It depends on the nature of the metal.
• (ii) Threshold Frequency (ν₀): It is the minimum frequency of incident electromagnetic radiation required to cause photoelectric emission from a given metal surface. If ν < ν₀, no emission occurs.
• (iii) Stopping Potential (V₀): It is the minimum negative (retarding) potential applied to the collector plate relative to the emitter plate at which the photoelectric current becomes exactly zero. It measures the maximum kinetic energy of emitted photoelectrons (K_max = e V₀).
Wave theory fails to explain photoelectric effect due to the following reasons:
1. Kinetic Energy vs Intensity: Wave theory predicts that higher light intensity spreads more wave energy, increasing the kinetic energy of emitted electrons. Experiments show kinetic energy depends solely on frequency, not intensity.
2. Threshold Frequency: Wave theory predicts that light of any frequency should emit electrons if intensity is high enough. Experiments show no emission occurs below threshold frequency ν₀ regardless of intensity.
3. Instantaneous Emission: Wave theory predicts a measurable time delay while an electron absorbs continuous wave energy over a large surface area. Experiments show photoelectric emission is virtually instantaneous (< 10⁻⁹ s).
Textbook Chapter End Exercise Questions
Given:
• Work function (ϕ₀) = 2.14 eV = 2.14 × 1.6 × 10⁻¹⁹ J = 3.424 × 10⁻¹⁹ J
• Incident frequency (ν) = 6.0 × 10¹⁴ Hz
• Planck's constant (h) = 6.63 × 10⁻³⁴ J s
• Mass of electron (m) = 9.1 × 10⁻³¹ kg
Part (a): Maximum Kinetic Energy (K_max)
E = h ν = (6.63 × 10⁻³⁴) × (6.0 × 10¹⁴) = 3.978 × 10⁻¹⁹ J = 2.486 eV
K_max = E - ϕ₀ = 2.486 eV - 2.14 eV = 0.346 eV = 0.35 eV (or 5.54 × 10⁻²⁰ J)
Part (b): Stopping Potential (V₀)
e V₀ = K_max => V₀ = 0.35 V
Part (c): Maximum Speed (v_max)
K_max = (1/2) m (v_max)²
v_max = √(2 K_max / m) = √[(2 × 5.54 × 10⁻²⁰) / (9.1 × 10⁻³¹)] ≈ 3.49 × 10⁵ m/s
• Maximum Kinetic Energy = 0.35 eV
• Stopping Potential = 0.35 V
• Maximum Speed = 3.49 × 10⁵ m/s
Given:
• Accelerating Potential (V) = 100 V
Formula:
λ = 1.227 / √V nm
Calculation:
λ = 1.227 / √100 = 1.227 / 10 = 0.1227 nm = 1.227 Å
The de Broglie wavelength of the accelerated electron is 0.123 nm (or 1.227 Å).
Read More & Chapter Resources
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