Marks Total Assignment Compton, De Broglie, And Wave Particl

28marks Totalassignment 14compton De Broglie And Wave Particl

Complete each of the six partial statements below using the following guide; all you need to provide for an answer is PE, CS, BOTH, or NEITHER. • PE if the statement only applies to the Photoelectric Effect • CS if the statement only applies to Compton Scattering • BOTH if the statement only applies to both the Photoelectric Effect and Compton Scattering • NEITHER if the statement applies to Neither the Photoelectric Effect or Compton Scattering

a. Energy is conserved in _____. Answer: (1)

b. Photons are observed before and after the interaction in _____. Answer: (1)

c. Electrons are observed as the result of the experiment in _____. Answer: (1)

d. Angles are measured in the experiment in _____. Answer: (1)

e. Photons with very low energies such as 5.0 to 10.0 eV is observed in _____. Answer: (1)

f. Ionization occurs in _____. Answer: (2)

2. What quantity measured in the Compton effect experiment show the wave-particle duality of light? Answer: (5)

3. An X-ray with a frequency of 3.74 × 10²⁰ Hz is incident on a thin piece of metal. The lower frequency X-ray on the other side is observed deflected at 48°. What is the frequency of the deflected X-ray? Answer: (5)

4. A scientist changes the frequency of an incident X-ray to 4.50 × 10¹⁹ Hz and measures the deflected X-ray frequency of 4.32 × 10¹⁹ Hz. What was the angle of deflection? Answer: (2)

5. Can the equation E = pc be applied to particles? Why or why not? Answer: (3)

6. A stationary hydrogen atom with a mass of 1.67 × 10^-27 kg absorbs a photon of light with 10.2 eV. What is the velocity of the hydrogen atom after absorbing the photon in a perfectly inelastic collision? Answer: (2)

7. Describe the results of performing Young’s experiment with x-rays and then high-speed electrons. Answer: (2)

8. How do the results of performing Young’s experiment with x-rays and then high-speed electrons support the wave-particle model? Answer: (1)

9. All of the following quantities can be measured or calculated for light waves and subatomic particles except _____. A. momentum B. velocity C. frequency D. energy Answer: (3)

Paper For Above instruction

The exploration of wave-particle duality exemplifies some of the most fascinating concepts in quantum physics, revealing the dual nature of light and matter. This essay will analyze the core principles behind the Photoelectric Effect, Compton Scattering, and the evidence supporting wave-particle duality, as well as their implications in modern physics.

Comparison of the Photoelectric Effect and Compton Scattering

The photoelectric effect (PE), discovered by Heinrich Hertz and explained by Albert Einstein, presents the notion that photons, or quanta of light, can eject electrons from a metal surface when the incident light surpasses a threshold frequency. In this process, energy conservation is fundamental, aligning with the principle that energy before and after the event remains constant, thus "Energy is conserved in PE" (Answer: PE). Photons are observed before and after the interaction, emphasizing the particle-like nature of light, which justifies the answer "Photons are observed before and after the interaction in PE" (Answer: PE). Electrons are produced as a direct result of photon energy transfer, which is evident in the photoelectric experiment, leading to the answer "Electrons are observed as the result of the experiment in PE" (Answer: PE). The photoelectric effect involves measurement of the kinetic energy and emission angles of electrons, but it does not explicitly involve measuring angles of photons, which makes "Angles are measured in the experiment in PE" (Answer: PE) context-specific. Low-energy photons, such as those in the ultraviolet range (5–10 eV), are typical in PE, thus the answer is "Photons with very low energies such as 5.0 to 10.0 eV is observed in PE" (Answer: PE). Ionization, the complete removal of electrons from atoms or molecules, occurs efficiently during PE, supporting "Ionization occurs in PE" (Answer: NEITHER), since this process is more characteristic of ionizing radiation rather than the specific photon-electron interaction in PE, which does not necessarily involve ionization in every case.

Compton scattering (CS), demonstrated by Arthur Compton, involves the collision of high-energy photons with electrons, resulting in a change in the photon’s wavelength and energy, a hallmark of wave-particle duality. Energy conservation also applies in CS, with photons losing energy and electrons gaining kinetic energy, so "Energy is conserved in CS" (Answer: CS). Unlike PE, photons before and after scattering are observed and measured, making "Photons are observed before and after the interaction in CS" (Answer: CS) valid. Electrons recoiling from the collision are the primary particles observed in CS, marking "Electrons are observed as the result of the experiment in CS" (Answer: CS). Angles of deflection are crucial in CS to quantify momentum transfer, hence "Angles are measured in the experiment in CS" (Answer: CS). The perturbed photon with low energies (5 eV range) is not typical in CS, where high-energy X-ray photons are used, but the interaction involves measurement of scattered photon angles and energies. Ionization may occur in CS but is not the defining feature; thus "Ionization occurs in CS" (Answer: NEITHER).

Wave-Particle Duality Evidence in Compton Effect

The quantity measured in the Compton effect that highlights the wave-particle duality of light is the scattering angle combined with the change in wavelength, often encapsulated in the Compton wavelength shift formula. This demonstrates the particle-like behavior of photons as they possess momentum and impart momentum to electrons, supporting the duality concept (Answer: 5).

Frequency Changes and Wave-Particle Interactions

In the provided scenario, the initial X-ray frequency of 3.74 × 10²⁰ Hz results in a deflected X-ray at 48°, changing its frequency upon scattering. Using Compton’s formula, the scattered frequency can be calculated considering the wavelength shift and the scattering angle. This underscores the particle nature of photons as they transfer energy and momentum during scattering (Answer: 5).

Similarly, when the incident X-ray frequency shifts from 4.50 × 10¹⁹ Hz to 4.32 × 10¹⁹ Hz with a deflection angle measured, we employ the Compton scattering formula to determine the precise scattering angle. These experiments demonstrate how electromagnetic radiation exhibits both wave and particle characteristics, fundamental to wave-particle duality (Answer: 2).

Applicability of E=pc to Particles

The equation E=pc relates the energy and momentum of particles, especially photons which are massless, indicating it applies solely to particles that travel at the speed of light. For massive particles, the relativistic energy equation E² = (pc)² + (mc²)² applies. Therefore, E=pc applies to massless particles like photons but not to massive particles traveling at lower speeds. The reason is that E=pc neglects rest mass energy, making the statement "Can the equation E=pc be applied to particles? Why or why not?" answerable as "Yes, but only for massless particles" (Answer: 3).

Post-Absorption Velocity of Hydrogen atoms

When a hydrogen atom absorbs a photon of 10.2 eV, it gains energy and momentum resulting in a recoil motion. Conservation of momentum and energy can be used to derive its velocity after absorption. Since the kinetic energy acquired is small relative to the atom’s rest energy, the atom’s velocity is found via p=mv, leading to a small but measurable velocity change. The calculated velocity aligns with the principle of inelastic collision dynamics, indicating that the hydrogen atom attains a finite velocity after photon absorption (Answer: 2).

Young’s Double-Slit Experiment with X-rays and Electrons

Performing Young’s experiment with X-rays and high-speed electrons demonstrates observable interference patterns. X-rays, exhibiting wave behavior, produce clear interference fringes, confirming their wave nature. Similarly, high-energy electrons form interference patterns consistent with their wave-like properties. The experimental results show that both forms of radiation possess wave characteristics, reinforcing the wave-particle duality in quantum particles (Answer: 2).

Support for Wave-Particle Model

Executing Young’s experiment with X-rays and high-speed electrons supports the wave-particle duality by providing visual evidence of wave interference for particles traditionally considered as particles, like electrons, confirming that they exhibit wave properties at quantum scales. This duality is central to modern quantum mechanics, emphasizing that particles behave as waves under certain conditions and as particles under others, such as in the photoelectric effect or scattering phenomena (Answer: 1).

Quantities for Light and Subatomic Particles

All these properties—momentum, velocity, frequency, and energy—are measurable or calculable for both light waves and subatomic particles, except perhaps velocity in cases where relativistic effects complicate direct measurement, or when the particle’s velocity is not directly measurable. Nonetheless, in principle, all options listed (momentum, velocity, frequency, energy) can be determined for light and particles, making "velocity" the exception in some practical contexts, leading to the answer "D. energy" as the correct choice when considering the question's context.

Conclusion

Overall, experiments such as the photoelectric effect, Compton scattering, and Young’s interference tests solidify the concept of wave-particle duality fundamental to quantum physics. They illustrate that light and matter exhibit dual characteristics, behaving as waves in some circumstances and as discrete particles in others. These phenomena have profound implications for understanding the nature of the universe at microscopic levels and continue to drive advancements in quantum technology and particle physics.

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