Chapter 11: Dual Nature of Radiation and Matter Long Questions | physics Class 12 CBSE

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Chapter 11: Dual Nature of Radiation and Matter Long Questions | physics Class 12 CBSE | ByteNotes.in

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Question 1

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Analyse the three experimental observations in the photoelectric effect that cannot be explained by the wave theory of light, and explain how Einstein's photon model resolves each contradiction.

Wave theory predicts that Kmax should increase with intensity, but experiments show Kmax is independent of intensity and depends only on frequency. Einstein resolved this by showing each electron absorbs one photon of fixed energy hν; more photons (higher intensity) produce more electrons, not more energetic ones.
Wave theory cannot explain threshold frequency, since intense radiation of any frequency should eventually provide enough energy. Einstein's model gives ν₀ = φ₀/h; below this frequency each photon lacks the minimum energy φ₀ to liberate an electron regardless of photon number.
Wave theory predicts a time lag of hours for electrons to accumulate work-function energy from a continuous wavefront. Einstein's model makes emission instantaneous because a single photon is absorbed by a single electron in one elementary event (~10⁻⁹ s).
Wave theory predicts stopping potential should increase with intensity, but experiments show it is independent of intensity. In Einstein's picture, stopping potential eV₀ = hν − φ₀ depends solely on photon frequency and work function.
Overall, Einstein's quantisation of radiation energy into photons of energy hν elegantly accounts for all four anomalous observations, marking the birth of the quantum theory of light.

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Question 2

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Describe the experimental arrangement used to study the photoelectric effect and discuss how photocurrent varies with collector plate potential for different intensities of incident radiation.

The setup consists of an evacuated glass/quartz tube with a photosensitive emitter plate C and a collector plate A. Monochromatic light enters through a quartz window and falls on C. A variable battery maintains potential difference between C and A, measured by a voltmeter, while a microammeter measures the resulting photocurrent.
When the collector A is at positive potential, electrons emitted from C are attracted to A, producing photocurrent. As the accelerating potential increases, photocurrent increases until it reaches saturation, where all emitted electrons reach A.
Further increase in accelerating potential beyond saturation does not increase the current. Saturation current is proportional to the intensity of incident radiation since more photons produce more photoelectrons per second.
When a negative (retarding) potential is applied to A, only the most energetic electrons can overcome the repulsion and reach A. As the retarding potential increases, the photocurrent decreases rapidly.
At the stopping potential V₀, even the most energetic photoelectrons are stopped and the current becomes zero. For a given frequency, V₀ is the same for all three intensities I₁, I₂, I₃, confirming that stopping potential is independent of intensity.

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Question 3

Long Form

Compare and contrast the photon model with the wave model of light in the context of photoelectric effect, highlighting where each model succeeds or fails.

The wave model successfully explains interference, diffraction, and polarisation by treating light as a continuous electromagnetic wave with energy distributed uniformly over the wavefront. However, it fails completely to explain the photoelectric effect.
The wave model cannot account for the existence of threshold frequency, the independence of Kmax from intensity, or instantaneous emission. It predicts that maximum kinetic energy should grow with intensity and that all frequencies should eventually cause emission given enough time.
The photon model treats light as consisting of discrete energy packets (photons), each with energy hν. It explains all features of the photoelectric effect: threshold frequency (ν₀ = φ₀/h), independence of Kmax from intensity, and instantaneous emission through single-photon single-electron absorption.
The photon model, however, cannot explain interference and diffraction, which require the wave picture. Thus, neither model alone is complete; both are needed depending on the nature of the experiment being analysed.
This complementarity is the essence of wave-particle duality: light behaves as a wave in propagation phenomena (interference, diffraction) and as a particle (photon) in interaction phenomena (photoelectric effect, Compton effect).

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Question 4

Long Form

Derive the expression for threshold frequency from Einstein's photoelectric equation and explain how stopping potential is related to the frequency of incident radiation.

Einstein's photoelectric equation is Kmax = hν − φ₀, where Kmax is the maximum kinetic energy of the emitted photoelectron, hν is the photon energy, and φ₀ is the work function of the metal.
For photoelectric emission to occur, Kmax must be non-negative, i.e., hν ≥ φ₀. The minimum frequency for which emission is just possible (Kmax = 0) is the threshold frequency ν₀, giving hν₀ = φ₀, so ν₀ = φ₀/h.
Using Kmax = eV₀ (where V₀ is the stopping potential), Einstein's equation becomes eV₀ = hν − φ₀, or V₀ = (h/e)ν − φ₀/e. This shows V₀ varies linearly with ν.
The graph of V₀ versus ν is a straight line with slope h/e (universal, independent of metal) and x-intercept at ν₀. Metals with higher work functions have higher threshold frequencies.
Millikan used this linear relationship and measured the slope for sodium to determine h accurately, confirming Einstein's equation. The slope h/e is the same for all metals, validating the universality of Planck's constant.

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Question 5

Long Form

Explain the photon picture of electromagnetic radiation and list its key properties. How does this picture explain that photon energy is independent of intensity?

In the photon picture, radiation is not a continuous wave but consists of discrete energy packets called photons or quanta. Each photon carries energy E = hν, where h is Planck's constant and ν is the frequency, and momentum p = hν/c, travelling at speed c.
All photons of the same frequency have identical energy and momentum regardless of the source's intensity. Photons are electrically neutral and unaffected by electric or magnetic fields.
When intensity is increased for light of a given frequency, only the number of photons crossing a unit area per second (photon flux) increases; the energy of each individual photon remains fixed at hν.
In photon-particle collisions, total energy and total momentum are conserved. However, the number of photons is not necessarily conserved; a photon may be absorbed or a new one created during the interaction.
This picture directly explains the photoelectric observations: more photons (higher intensity) means more electrons emitted per second (higher photocurrent), but since each photon's energy is unchanged, the maximum kinetic energy of each electron remains the same, independent of intensity.

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Question 6

Long Form

Discuss de Broglie's hypothesis of matter waves. Derive the expression for de Broglie wavelength and show that it is also satisfied by a photon.

De Broglie proposed in 1924 that moving material particles have an associated wave character, arguing that if radiation shows dual nature, matter must also be symmetrical and exhibit both particle and wave properties.
He proposed the de Broglie relation: λ = h/p = h/mv, where λ is the matter wavelength, h is Planck's constant, m is the particle mass, and v is its speed. The left side (λ) is a wave attribute; the right side (p) is a particle attribute.
For a photon, the momentum is p = hν/c (as derived by Einstein). Substituting into λ = h/p gives λ = h/(hν/c) = c/ν, which is exactly the wavelength of the electromagnetic radiation of frequency ν.
Thus, the de Broglie relation is satisfied by photons, confirming its consistency. For a material particle like an electron (mass 9.11 × 10⁻³¹ kg) moving at 5.4 × 10⁶ m/s, λ ≈ 0.135 nm, comparable to X-ray wavelengths and detectable.
For macroscopic objects (e.g., a ball of mass 0.12 kg at 20 m/s), λ ≈ 2.76 × 10⁻³⁴ m, far beyond any measurement, explaining why macroscopic objects show no wave behaviour.

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Question 7

Long Form

Analyse the variation of stopping potential with frequency of incident radiation and explain what the graph between stopping potential and frequency reveals about the nature of photoelectric emission.

When the frequency of incident radiation is varied while keeping intensity constant, different stopping potentials are obtained for different frequencies but the saturation current remains the same. Higher frequency radiation gives a more negative stopping potential.
Plotting stopping potential V₀ on the y-axis against frequency ν on the x-axis gives a straight line for a given photosensitive material, confirming the linear relationship V₀ = (h/e)ν − φ₀/e derived from Einstein's equation.
The slope of this line is h/e, which is universal and independent of the metal used. The x-intercept gives the threshold frequency ν₀ below which V₀ = 0 and no emission occurs. Different metals have different x-intercepts (threshold frequencies) due to different work functions.
The fact that the slope is the same for all metals while the x-intercept varies with the metal is strong experimental evidence for Einstein's photon model and for the universality of Planck's constant h.
This graph is crucial because it shows that maximum kinetic energy (proportional to V₀) depends linearly on frequency, proving that photon energy is proportional to frequency, which is a direct confirmation of E = hν.

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Question 8

Long Form

Describe the contributions of Hertz, Hallwachs, Lenard, and Einstein to the understanding of the photoelectric effect, in chronological order.

In 1887, Hertz discovered the photoelectric effect while investigating electromagnetic waves. He observed that high-voltage sparks were enhanced when the emitter plate was illuminated by ultraviolet light from an arc lamp, indicating that light facilitated the escape of charged particles.
Hallwachs (1888) connected a negatively charged zinc plate to an electroscope and found that ultraviolet light caused the plate to lose charge, and an uncharged plate became positively charged — he concluded that negatively charged particles were emitted.
Lenard (1886–1902) demonstrated that current flowed in an evacuated tube when ultraviolet radiation fell on the emitter plate, stopping immediately when radiation was removed. He also established the existence of threshold frequency: no emission if incident frequency was below a minimum value characteristic of the emitter material.
Einstein (1905) proposed the radical hypothesis of light quanta (photons), each of energy hν, and used it to formulate the photoelectric equation Kmax = hν − φ₀. This explained all the experimental features that classical wave theory had failed to account for.
Millikan (1906–1916) initially tried to disprove Einstein's equation but instead confirmed it with high precision, measured h accurately, and validated the photon model over a wide range of frequencies and materials.

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Question 9

Long Form

Explain why the de Broglie wavelength is significant for electrons and protons but not for macroscopic objects. Support your answer with numerical reasoning from the chapter.

The de Broglie wavelength is λ = h/mv. For wave behaviour to be observable, the wavelength must be comparable to the size of the objects or slits that the particle interacts with (e.g., atomic spacings ~0.1–1 nm in crystals).
For an electron (m = 9.11 × 10⁻³¹ kg) moving at 5.4 × 10⁶ m/s, λ = 0.135 nm, which is comparable to X-ray wavelengths and atomic plane spacings. This makes diffraction and wave behaviour of electrons experimentally detectable.
For a ball of mass 0.150 kg moving at 30 m/s, λ = h/mv ≈ 1.47 × 10⁻³⁴ m. This is about 10⁻¹⁹ times the size of a proton, completely beyond any measurement, so no wave effects are observable.
The key reason is that macroscopic objects have very large masses and momenta compared to subatomic particles. Since λ = h/p and h is extremely small (6.626 × 10⁻³⁴ J s), large p makes λ vanishingly small.
Thus, the wave character of matter is significant and measurable only in the sub-atomic domain (electrons, protons, neutrons), which is the domain of quantum mechanics, while classical mechanics suffices for macroscopic objects.

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Question 10

Long Form

Discuss the dual nature of radiation with appropriate examples showing when the wave nature and when the particle nature of light is relevant.

Radiation exhibits a dual nature: it behaves as a wave in some experiments and as a particle (photon) in others. This is not a contradiction but a complementarity — the nature of the experiment determines which description is appropriate.
Wave nature is evident in interference (e.g., Young's double-slit experiment showing bright and dark fringes), diffraction (bending of light around edges), and polarisation (orientation of electric field oscillations). These phenomena require a continuous wave description and cannot be explained by particles.
Particle nature is evident in the photoelectric effect (one photon ejects one electron), the Compton effect (X-ray photons scatter off electrons with momentum transfer), and absorption/emission spectra. These require discrete energy packets and cannot be explained by waves.
Even in everyday vision, both descriptions are relevant: the gathering and focusing of light by the eye-lens is explained by the wave picture, while absorption by retinal rods and cones requires the photon picture.
The reconciliation lies in quantum mechanics: light is neither purely a wave nor purely a particle but a quantum entity. The concept of wave-particle duality is fundamental to modern physics and extends to matter as well through de Broglie's hypothesis.

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Chapter 11: Dual Nature of Radiation and Matter | Long Questions

Analyse the three experimental observations in the photoelectric effect that cannot be explained by the wave theory of light, and explain how Einstein's photon model resolves each contradiction.

Describe the experimental arrangement used to study the photoelectric effect and discuss how photocurrent varies with collector plate potential for different intensities of incident radiation.

Compare and contrast the photon model with the wave model of light in the context of photoelectric effect, highlighting where each model succeeds or fails.

Derive the expression for threshold frequency from Einstein's photoelectric equation and explain how stopping potential is related to the frequency of incident radiation.

Explain the photon picture of electromagnetic radiation and list its key properties. How does this picture explain that photon energy is independent of intensity?

Discuss de Broglie's hypothesis of matter waves. Derive the expression for de Broglie wavelength and show that it is also satisfied by a photon.

Analyse the variation of stopping potential with frequency of incident radiation and explain what the graph between stopping potential and frequency reveals about the nature of photoelectric emission.

Describe the contributions of Hertz, Hallwachs, Lenard, and Einstein to the understanding of the photoelectric effect, in chronological order.

Explain why the de Broglie wavelength is significant for electrons and protons but not for macroscopic objects. Support your answer with numerical reasoning from the chapter.

Discuss the dual nature of radiation with appropriate examples showing when the wave nature and when the particle nature of light is relevant.

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