Class 12 Physics Notes Chapter 11 (Dual Nature of Radiation and Matter) – Examplar Problems (English) Book
Alright students, let's focus on Chapter 11: Dual Nature of Radiation and Matter. This is a fascinating chapter that bridges classical and modern physics, and it's crucial for your exams. We'll break down the key concepts from the NCERT perspective, focusing on what you need for competitive government exams.
Chapter 11: 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 (explained by Planck), etc., could not be explained by the wave nature of light alone.
- Similarly, experiments later showed that particles like electrons can exhibit wave-like properties (e.g., diffraction).
- This led to the concept of Wave-Particle Duality: Radiation (like light) and matter (like electrons) can exhibit both wave and particle characteristics depending on the experimental context.
2. Electron Emission:
- For electrons to be emitted from a metal surface, they need sufficient energy to overcome the attractive forces holding them within the metal.
- Work Function (Φ₀ or W): The minimum energy required by an electron to just escape from the metal surface is called the work function of the metal. It's measured in electron volts (eV). 1 eV = 1.602 × 10⁻¹⁹ Joules.
- Work function depends on the nature of the metal and the condition of its surface.
- Types of Electron Emission:
- (a) Thermionic Emission: Electrons emitted by heating the metal.
- (b) Field Emission: Electrons emitted by applying a very strong electric field (≈ 10⁸ V/m).
- (c) Photoelectric Emission: Electrons emitted when light (electromagnetic radiation) of suitable frequency falls on the metal surface. These emitted electrons are called photoelectrons.
3. Photoelectric Effect:
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Hertz's Observations (1887): Noticed that sparks occurred more readily across a detector loop when it was illuminated by UV light from the transmitter spark gap.
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Hallwachs' and Lenard's Observations (1886-1902):
- UV light on a negatively charged zinc plate caused it to lose its charge.
- UV light on an uncharged zinc plate caused it to become positively charged.
- UV light on a positively charged zinc plate caused it to become even more positively charged (or rather, enhanced its positive charge).
- Conclusion: Negatively charged particles (electrons) were being emitted under UV illumination.
- Lenard studied the variation of photocurrent with collector plate potential and light intensity/frequency.
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Experimental Study of Photoelectric Effect - Key Observations:
- (i) Effect of Intensity of Light: For a fixed frequency, the photocurrent (number of photoelectrons emitted per second) is directly proportional to the intensity of the incident radiation. More intense light means more photons, leading to more electron emissions.
- (ii) Effect of Potential:
- For a given frequency and intensity, as the positive potential of the collector plate increases, the photocurrent increases until it reaches a saturation current (all emitted electrons are collected).
- If the collector plate potential is made negative, the photocurrent decreases.
- Stopping Potential (V₀): The minimum negative (retarding) potential applied to the collector plate for which the photocurrent becomes zero. At this potential, even the most energetic photoelectrons are repelled back.
- The maximum kinetic energy of the emitted photoelectrons is related to the stopping potential: K_max = e V₀.
- (iii) Effect of Frequency of Incident Radiation:
- For a given intensity, the stopping potential (V₀), and hence the maximum kinetic energy (K_max) of photoelectrons, increases linearly with the frequency (ν) of the incident radiation.
- Threshold Frequency (ν₀): There exists a minimum frequency, called the threshold frequency, below which no photoelectric emission occurs, no matter how high the intensity. This frequency is characteristic of the metal.
- (iv) Instantaneous Process: Photoelectric emission is an almost instantaneous process (time lag < 10⁻⁹ s), even for very low intensities (provided ν > ν₀).
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Failure of Wave Theory to Explain Photoelectric Effect:
- (Intensity): Wave theory predicts that higher intensity (more energy per unit area per time) should impart greater kinetic energy to electrons, but experiments show K_max depends only on frequency, not intensity. Intensity only affects the number of electrons (photocurrent).
- (Frequency): Wave theory suggests that light of any frequency, if intense enough, should be able to eject electrons. Experiments show a threshold frequency (ν₀) exists.
- (Kinetic Energy): Wave theory implies energy is absorbed continuously over the wavefront, so electrons should gain energy gradually. It cannot explain why K_max depends linearly on frequency.
- (Time Lag): Wave theory predicts a significant time lag for electrons to accumulate enough energy, especially at low intensities. Experiments show emission is instantaneous.
4. Einstein's Photoelectric Equation: Energy Quantum of Radiation
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Planck's Quantum Theory (1900): Proposed that energy exchange in blackbody radiation occurs in discrete packets called quanta (Energy E = hν, where h is Planck's constant = 6.626 × 10⁻³⁴ J s).
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Einstein's Extension (1905): Proposed that light itself consists of discrete energy packets called photons. The energy of each photon is E = hν = hc/λ, where c is the speed of light and λ is the wavelength.
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Photon Properties:
- Travels at the speed of light (c) in vacuum.
- Has zero rest mass.
- Carries energy E = hν.
- Carries momentum p = E/c = hν/c = h/λ.
- Is electrically neutral.
- Energy and momentum are conserved in photon-particle collisions.
- Intensity of light depends on the number of photons crossing unit area per unit time.
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Einstein's Explanation of Photoelectric Effect:
- Photoelectric emission results from the collision between a photon and an electron.
- In such a collision, a photon gives its entire energy (hν) to a single electron.
- Part of this energy is used by the electron to overcome the work function (Φ₀) of the metal.
- The remaining energy appears as the kinetic energy of the emitted electron.
- For the electron with maximum kinetic energy (K_max), the equation is:
K_max = hν - Φ₀ (Einstein's Photoelectric Equation) - Since K_max = eV₀ and Φ₀ = hν₀ (where ν₀ is the threshold frequency), we can write:
eV₀ = hν - hν₀
or K_max = h(ν - ν₀)
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Success of Einstein's Equation:
- Intensity: Higher intensity means more photons per second, thus more collisions and more photoelectrons (higher photocurrent). Photon energy (hν) remains the same, so K_max is unchanged.
- Frequency: If hν < Φ₀ (i.e., ν < ν₀), the electron doesn't get enough energy to escape, explaining the threshold frequency. If ν > ν₀, K_max increases linearly with ν (K_max = hν - Φ₀).
- Time Lag: Energy transfer is instantaneous in the photon-electron collision, explaining the lack of time lag.
5. Wave Nature of Matter: de Broglie Hypothesis
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Louis de Broglie's Hypothesis (1924): If radiation (like light) can exhibit dual wave-particle nature, then matter (like electrons, protons, atoms) should also exhibit dual nature. Moving particles should be associated with a wave.
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de Broglie Wavelength (λ): The wavelength associated with a particle of momentum 'p' is given by:
λ = h / p
where h is Planck's constant. -
For a particle of mass 'm' moving with velocity 'v':
λ = h / (mv) -
de Broglie Wavelength of an Electron:
If an electron (mass m, charge e) is accelerated from rest through a potential difference V, its kinetic energy K = eV.
Momentum p = √(2mK) = √(2meV)
So, the de Broglie wavelength is:
λ = h / √(2meV)
Substituting values for h, m (mass of electron = 9.1 × 10⁻³¹ kg), and e (charge of electron = 1.6 × 10⁻¹⁹ C):
λ ≈ 1.227 / √V nm (where V is in Volts) -
Significance: The wave nature of matter is significant only for microscopic particles (like electrons) because their mass is small, leading to a measurable wavelength. For macroscopic objects, the wavelength is extremely small and undetectable.
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Davisson and Germer Experiment (1927):
- Experimentally confirmed the wave nature of electrons.
- They observed diffraction patterns when a beam of electrons was scattered off a nickel crystal, similar to X-ray diffraction.
- The measured wavelength from the diffraction pattern matched the de Broglie wavelength calculated using the accelerating potential.
6. Heisenberg's Uncertainty Principle (Brief Mention):
- It is impossible to measure simultaneously both the position and the momentum of a particle with absolute accuracy.
- If Δx is the uncertainty in position and Δp is the uncertainty in momentum, then:
Δx Δp ≥ ħ/2 (where ħ = h/2π) - This principle is a fundamental consequence of wave-particle duality and sets a limit on the precision of measurements at the quantum level.
7. Conclusion: Wave-Particle Duality
- Both matter and radiation exhibit dual behaviour.
- Which aspect (wave or particle) is observed depends on the experiment being performed.
- The wave nature (λ = h/p) and particle nature (E = hν) are linked by Planck's constant 'h'.
Multiple Choice Questions (MCQs)
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The minimum energy required to eject an electron from a metal surface is called:
(a) Kinetic Energy
(b) Photon Energy
(c) Work Function
(d) Stopping Potential -
In the photoelectric effect, the number of photoelectrons emitted per second (photocurrent) is directly proportional to the:
(a) Frequency of incident light
(b) Intensity of incident light
(c) Work function of the metal
(d) Stopping potential -
The stopping potential (V₀) in photoelectric emission depends on:
(a) Intensity of incident light only
(b) Frequency of incident light only
(c) Both intensity and frequency
(d) Neither intensity nor frequency -
Einstein's Photoelectric Equation is given by (K_max = max kinetic energy, ν = frequency, Φ₀ = work function):
(a) K_max = hν + Φ₀
(b) K_max = hν / Φ₀
(c) K_max = Φ₀ - hν
(d) K_max = hν - Φ₀ -
Which phenomenon most effectively demonstrates the particle nature of light?
(a) Diffraction
(b) Interference
(c) Polarization
(d) Photoelectric Effect -
The rest mass of a photon is:
(a) Infinite
(b) Equal to electron mass
(c) Zero
(d) Dependent on its frequency -
The de Broglie wavelength associated with a particle is given by:
(a) λ = mc²/h
(b) λ = h / mv
(c) λ = h / eV
(d) λ = mv / h -
If an electron is accelerated through a potential difference V, its de Broglie wavelength is proportional to:
(a) V
(b) √V
(c) 1/√V
(d) 1/V -
The Davisson and Germer experiment confirmed the:
(a) Particle nature of light
(b) Wave nature of electrons
(c) Existence of photons
(d) Quantization of charge -
According to de Broglie's hypothesis, which of the following objects would have the smallest wavelength when moving at the same speed?
(a) An electron
(b) A proton
(c) An alpha particle
(d) A cricket ball
Answer Key for MCQs:
- (c) Work Function
- (b) Intensity of incident light
- (b) Frequency of incident light only
- (d) K_max = hν - Φ₀
- (d) Photoelectric Effect
- (c) Zero
- (b) λ = h / mv
- (c) 1/√V
- (b) Wave nature of electrons
- (d) A cricket ball (Since λ = h/mv, the largest mass 'm' will have the smallest wavelength 'λ' for the same speed 'v').
Make sure you understand the concepts behind these points and formulas, especially the experimental results of the photoelectric effect and how Einstein's equation explains them, along with the de Broglie hypothesis and its verification. Good luck with your preparation!