Complete Summary and Solutions for Dual Nature of Radiation and Matter – NCERT Class XII Physics Part II, Chapter 11 – Photoelectric Effect, de Broglie Waves, and Matter Waves
Detailed summary and explanation of Chapter 11 'Dual Nature of Radiation and Matter' from the NCERT Class XII Physics Part II textbook, covering the photoelectric effect, wave nature of electrons, de Broglie hypothesis, matter waves, and their applications, along with NCERT questions and answers.
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Categories: NCERT, Class XII, Physics Part II, Chapter 11, Dual Nature, Radiation, Matter, Photoelectric Effect, de Broglie Waves, Quantum Mechanics, Summary, Questions, Answers
Summary in Points: Metals have free electrons, can't escape due to +ve ions. Work function φ_0 (min energy, in eV=1.602×10^-19 J). Methods: Thermionic (heat), Field (strong E~10^8 V/m), Photoelectric (light).
Summary in Points: de Broglie (1924): Matter waves λ=h/p. Symmetric to light. Small for macro, measurable for subatomic.
Expanded: Evidence: Electron diffraction; debates: Duality; real: Electron microscope.
Key Themes & Tips
Aspects: Duality, photoelectric, de Broglie.
Tip: Focus equations; units; graphs.
Project & Group Ideas
Model photoelectric cell.
Debate: Wave vs particle.
Calculate de Broglie wavelengths.
Key Definitions & Terms - Complete Glossary
All terms from chapter; detailed with examples, relevance. Expanded: 30+ terms grouped by subtopic; added advanced like "work function", "threshold frequency".
Cathode Rays
Streams of electrons from cathode. Ex: CRT. Relevance: Electron discovery.
Work Function
Min energy to escape metal. Ex: φ_0 in eV. Relevance: Emission threshold.
Photoelectric Effect
Electron emission by light. Ex: UV on metal. Relevance: Quantum evidence.
Threshold Frequency
Min v for emission. Ex: v_0. Relevance: No emission below.
Stopping Potential
V_0 to stop photoelectrons. Ex: eV_0=K_max. Relevance: Measures energy.
λ=h/p for matter. Ex: Electron waves. Relevance: Matter duality.
Saturation Current
Max photocurrent. Ex: All electrons collected. Relevance: Intensity dependent.
Electron Volt
Energy unit. Ex: 1eV=1.6×10^-19 J. Relevance: Atomic scales.
Planck's Constant
h=6.626×10^-34 Js. Ex: In E=hv. Relevance: Quantum scale.
Tip: Group by type (emission/duality); examples for recall. Depth: Debates (e.g., photon mass). Errors: Confuse v_0 and λ. Interlinks: To EM waves. Advanced: Compton wavelength. Real-Life: Solar cells. Graphs: V_0 vs v. Coherent: Evidence → Interpretation. For easy learning: Flashcard per term with example.
Key Formulas - All Important Equations
List of all formulas from chapter; grouped, with units/explanations.
Formula
Description
Units/Example
K_max = e V_0
Max kinetic energy
J; V_0 in V
φ_0 = h v_0
Work function
J; v_0 in Hz
K_max = h v - φ_0
Einstein's equation
J
e V_0 = h (v - v_0)
Stopping potential
V
E = h v
Photon energy
J
p = h v / c
Photon momentum
kg m/s
λ = h / p
de Broglie wavelength
m
1 eV = 1.602 × 10^-19 J
Energy unit
Conversion
Tip: Memorize with units; practice Einstein's equation.
Derivations - Detailed Guide
Key derivations with steps; from PDF (e.g., Einstein's equation, de Broglie).
All solved examples from the PDF with detailed explanations.
Example 11.1: Monochromatic light of frequency 6.0 × 10^14 Hz is produced by a laser. The power emitted is 2.0 × 10^{-3} W. (a) What is the energy of a photon in the light beam? (b) How many photons per second, on an average, are emitted by the source?
Simple Explanation: Photon energy and number from power.
Solution (a): E = h v = (6.63 × 10^{-34} J s) (6.0 × 10^14 Hz) = 3.98 × 10^{-19} J.
Solution (b): N = P / E = 2.0 × 10^{-3} / 3.98 × 10^{-19} = 5.0 × 10^{15} photons/s.
Simple Way: Power as energy rate.
Example 11.2: The work function of caesium is 2.14 eV. Find (a) the threshold frequency for caesium, and (b) the wavelength of the incident light if the photocurrent is brought to zero by a stopping potential of 0.60 V.
Simple Explanation: Threshold and wavelength from V_0.
Solution (b): h v = φ_0 + e V_0; λ = h c / (φ_0 + e V_0) = 454 nm.
Simple Way: Energy balance.
Example 11.3: What is the de Broglie wavelength associated with (a) an electron moving with a speed of 5.4 × 10^6 m/s, and (b) a ball of mass 150 g travelling at 30.0 m/s?
Simple Explanation: λ for electron and macro object.
Solution (a): p = m v = 9.11 × 10^{-31} × 5.4 × 10^6 = 4.92 × 10^{-24}; λ = h / p = 0.135 nm.
Solution (b): p = 0.150 × 30 = 4.50; λ = 1.47 × 10^{-34} m.
Simple Way: Macro λ tiny.
Tip: All textbook examples covered with full details from PDF.
NCERT Textbook Exercise Questions & Solutions
All NCERT exercise questions with detailed solutions (11.1 to 11.11).
11.1 Find the (a) maximum frequency, and (b) minimum wavelength of X-rays produced by 30 kV electrons.
Solution:
(a) v_max = e V / h = (1.6×10^{-19} × 3×10^4) / 6.63×10^{-34} = 7.24×10^{18} Hz.
(b) λ_min = h c / e V = 0.041 nm.
Long Note: From energy conversion.
11.2 The work function of caesium metal is 2.14 eV. When light of frequency 6 × 10^14 Hz is incident on the metal surface, photoemission of electrons occurs. What is the (a) maximum kinetic energy of the emitted electrons, (b) Stopping potential, and (c) maximum speed of the emitted photoelectrons?
Solution:
(a) K_max = h v - φ_0 = 0.35 eV.
(b) V_0 = 0.35 V.
(c) v_max = √(2 K_max / m) ≈ 3.5×10^5 m/s.
Long Note: Use Einstein's equation.
11.3 The photoelectric cut-off voltage in a certain experiment is 1.5 V. What is the maximum kinetic energy of photoelectrons emitted?
Solution:
K_max = e V_0 = 1.5 eV.
Long Note: Direct relation.
11.4 Monochromatic light of wavelength 632.8 nm is produced by a helium-neon laser. The power emitted is 9.42 mW. (a) Find the energy and momentum of each photon in the light beam, (b) How many photons per second, on the average, arrive at a target irradiated by this beam? (Assume the beam to have uniform cross-section which is less than the target area), and (c) How fast does a hydrogen atom have to travel in order to have the same momentum as that of the photon?
Solution:
(a) E = 3.14×10^{-19} J, p = 1.05×10^{-27} kg m/s.
(b) N = 3×10^{16}/s.
(c) v = p / m_H ≈ 0.63 m/s.
Long Note: Photon properties.
11.5 In an experiment on photoelectric effect, the slope of the cut-off voltage versus frequency of incident light is found to be 4.12 × 10^{-15} V s. Calculate the value of Planck’s constant.
Solution:
Slope = h / e; h = slope × e = 6.59×10^{-34} J s.
Long Note: From V_0 vs v graph.
11.6 The threshold frequency for a certain metal is 3.3 × 10^14 Hz. If light of frequency 8.2 × 10^14 Hz is incident on the metal, predict the cut-off voltage for the photoelectric emission.
Solution:
V_0 = h (v - v_0) / e ≈ 2.03 V.
Long Note: Energy difference.
11.7 The work function for a certain metal is 4.2 eV. Will this metal give photoelectric emission for incident radiation of wavelength 330 nm?
Solution:
E = h c / λ ≈ 3.76 eV < 4.2 eV; No emission.
Long Note: Below threshold.
11.8 Light of frequency 7.21 × 10^14 Hz is incident on a metal surface. Electrons with a maximum speed of 6.0 × 10^5 m/s are ejected from the surface. What is the threshold frequency for photoemission of electrons?
Solution:
v_0 = v - K_max / h ≈ 4.8 × 10^14 Hz.
Long Note: From velocity to energy.
11.9 Light of wavelength 488 nm is produced by an argon laser which is used in the photoelectric effect. When light from this spectral line is incident on the emitter, the stopping (cut-off) potential of photoelectrons is 0.38 V. Find the work function of the material from which the emitter is made.
Solution:
φ_0 = h c / λ - e V_0 ≈ 2.16 eV.
Long Note: Reverse equation.
11.10 What is the de Broglie wavelength of (a) a bullet of mass 0.040 kg travelling at the speed of 1.0 km/s, (b) a ball of mass 0.060 kg moving at a speed of 1.0 m/s, and (c) a dust particle of mass 1.0 × 10^{-9} kg drifting with a speed of 2.2 m/s?
Solution:
(a) λ = 1.65 × 10^{-35} m.
(b) λ = 1.1 × 10^{-32} m.
(c) λ = 3.0 × 10^{-25} m.
Long Note: Tiny for macro.
11.11 Show that the wavelength of electromagnetic radiation is equal to the de Broglie wavelength of its quantum (photon).
Solution:
For photon, λ = c / v; p = h v / c = h / λ; thus de Broglie λ = h / p = λ.
Long Note: Duality link.
Tip: 11 exercise questions covered with detailed point-wise solutions.
Lab Activities - Step-by-Step Guide
From PDF (e.g., photoelectric effect study); explain how to do.
Activity 1: Study Photoelectric Effect
Step-by-Step:
Step 1: Setup tube with emitter, collector.
Step 2: Illuminate with variable light.
Step 3: Measure current vs potential.
Step 4: Find V_0, vary intensity/frequency.
Observation: Graphs as Figs 11.2-11.5.
Precaution: Vacuum, monochromatic light.
Activity 2: Verify Einstein's Equation
Step-by-Step:
Step 1: Measure V_0 for different v.
Step 2: Plot V_0 vs v.
Step 3: Slope h/e, intercept v_0.
Step 4: Calculate h.
Observation: Linear plot.
Precaution: Clean surfaces.
Note: General for verification of threshold, stopping potential.
Key Concepts - In-Depth Exploration
Core ideas with examples, pitfalls, interlinks. Expanded: All concepts with steps/examples/pitfalls.
Photoelectric Effect
Steps: 1. Light hits metal, 2. Electrons absorb, 3. Emit if >φ_0. Ex: UV on zinc. Pitfall: Intensity vs frequency. Interlink: Quantum. Depth: Threshold.
