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Chapter Analysis
Advanced16 pages • EnglishQuick Summary
The chapter 'Dual Nature Of Radiation And Matter' explores the concept of wave-particle duality, focusing on the photoelectric effect and wave theory of light. It discusses the work of scientists like Einstein and de Broglie, whose contributions were crucial to developing the quantum theory and understanding the behavior of photons and electrons. The chapter explains phenomena like photoelectric emission and introduces de Broglie's hypothesis that particles have wave-like characteristics.
Key Topics
- •Wave-particle duality
- •Photoelectric effect
- •Einstein's photoelectric equation
- •De Broglie's hypothesis
- •Quantum mechanics
- •Matter waves
Learning Objectives
- ✓Understand the concept of wave-particle duality and its implications.
- ✓Explain the photoelectric effect and its significance in quantum theory.
- ✓Describe de Broglie's hypothesis of matter waves.
- ✓Analyze experiments that demonstrate the wave nature of particles.
- ✓Recognize the role of different parameters affecting photoelectric emission.
Questions in Chapter
Find the (a) maximum frequency, and (b) minimum wavelength of X-rays produced by 30 kV electrons.
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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?
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The photoelectric cut-off voltage in a certain experiment is 1.5 V. What is the maximum kinetic energy of photoelectrons emitted?
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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?
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In an experiment on photoelectric effect, the slope of the cut-off voltage versus frequency of incident light is 4.12 × 10^-15 V s. Calculate the Planck's constant.
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Additional Practice Questions
What is the relation between stopping potential and frequency of incident light in photoelectric effect?
mediumAnswer: In photoelectric effect, the stopping potential is directly proportional to the frequency of the incident light, as given by the equation eV = hν - φ0, where V is the stopping potential, h is Planck's constant, ν is the frequency, and φ0 is the work function.
Explain the significance of Einstein's photoelectric equation.
mediumAnswer: Einstein's photoelectric equation, Kmax = hν - φ0, explains the phenomena of photoelectric emission as a result of light quanta (photons) interacting with electrons in a material. It highlights the energy conservation principle by stating that the maximum kinetic energy of the emitted photoelectron is the energy of the photon minus the work function of the material.
How does the dual nature of particles explain phenomena in quantum mechanics?
hardAnswer: The dual nature of particles refers to their particle-like and wave-like behavior. This duality is essential in quantum mechanics, explaining phenomena such as electron diffraction and interference patterns that cannot be described by classical mechanics. It is encapsulated in de Broglie's hypothesis, which posits that the wavelength associated with a particle is inversely proportional to its momentum.
Describe an experiment that demonstrates the wave nature of electrons.
hardAnswer: The Davisson-Germer experiment demonstrated the wave nature of electrons by showing that electrons exhibit diffraction patterns similar to X-rays when they interact with a crystalline structure, which confirmed de Broglie's hypothesis about the wave nature of particles.
What is the significance of the threshold frequency in the photoelectric effect?
mediumAnswer: The threshold frequency is the minimum frequency of incident light required to emit electrons from a given metal surface. It signifies the limit below which no photoelectric emission occurs regardless of the light intensity, as the photon energy is insufficient to overcome the material's work function.