Textbook Question
Determine the energy of 1 mol of photons for each kind of light. (Assume three significant figures.) a. infrared radiation (1500 nm) b. visible light (500 nm) c. ultraviolet radiation (150 nm)
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Ch.7 - Quantum-Mechanical Model of the Atom
Chapter 7, Problem 48
What happens to the interference pattern if we attempt to determine which slit the electron passes through using a laser placed directly behind the slits? Additionally, what happens to the interference pattern described in Problem 47 if the rate of electrons passing through the slits is reduced to one electron per hour?
Verified step by step guidance1
Step 1: Understand the concept of wave-particle duality, which states that particles like electrons exhibit both wave-like and particle-like properties.
Step 2: Recognize that the interference pattern is a result of the wave-like behavior of electrons, where they pass through both slits simultaneously, creating an interference pattern on the detection screen.
Step 3: Consider the effect of measuring which slit the electron passes through. According to the principle of complementarity, attempting to measure the path of the electron collapses its wave function, causing it to behave more like a particle.
Step 4: Realize that when a laser is used to determine the path of the electron, the act of measurement disturbs the electron's wave function, resulting in the disappearance of the interference pattern.
Step 5: Analyze the scenario where electrons pass through the slits one at a time. Even at a rate of one electron per hour, if no measurement is made to determine the path, the interference pattern will still form over time, as each electron interferes with itself.
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Wave-Particle Duality
Wave-particle duality is a fundamental concept in quantum mechanics that describes how particles, such as electrons, exhibit both wave-like and particle-like properties. When not observed, electrons can create interference patterns typical of waves, but when a measurement is made to determine their path, they behave like particles, collapsing the wave function and eliminating the interference pattern.
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05:19
Subatomic Particles
Quantum Measurement
Quantum measurement refers to the process of observing a quantum system, which fundamentally alters its state. In the context of the double-slit experiment, attempting to measure which slit an electron passes through causes the system to lose its wave-like behavior, resulting in the disappearance of the interference pattern. This highlights the observer effect in quantum mechanics.
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Single Electron Interference
Single electron interference occurs when electrons are sent through a double-slit apparatus one at a time. Even at low rates, individual electrons can still create an interference pattern over time, demonstrating their wave-like nature. This phenomenon illustrates that the interference pattern emerges from the collective behavior of many single electrons, reinforcing the concept of wave-particle duality.
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Related Practice
Textbook Question
How much energy is contained in 1 mol of each? a. X-ray photons with a wavelength of 0.135 nm b. γ-ray photons with a wavelength of 2.15×10–5 nm
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Textbook Question
Sketch the interference pattern that results from the diffraction of electrons passing through two closely spaced slits.
Textbook Question
The resolution limit of a microscope is roughly equal to the wavelength of light used in producing the image. Electron microscopes use an electron beam (in place of photons) to produce much higher resolution images, about 0.20 nm in modern instruments. Assuming that the resolution of an electron microscope is equal to the de Broglie wavelength of the electrons used, to what speed must the electrons be accelerated to obtain a resolution of 0.20 nm?
Textbook Question
The smallest atoms can themselves exhibit quantum-mechanical behavior. Calculate the de Broglie wavelength (in pm) of a hydrogen atom traveling at 475 m/s.