Domanda del libro di testo
An experiment has four possible outcomes, labeled A to D. The probability of A is PA = 40% and of B is PB = 30%. Outcome C is twice as probable as outcome D. What are the probabilities PC and PD?
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Ch 39: Wave Functions and Uncertainty
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796
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TOC.tableOfContents
- Ch 01: Concepts of Motion35
- Ch 02: Kinematics in One Dimension75
- Ch 03: Vectors and Coordinate Systems58
- Ch 04: Kinematics in Two Dimensions60
- Ch 05: Force and Motion23
- Ch 06: Dynamics I: Motion Along a Line53
- Ch 07: Newton's Third Law27
- Ch 08: Dynamics II: Motion in a Plane52
- Ch 09: Work and Kinetic Energy56
- Ch 10: Interactions and Potential Energy50
- Ch 11: Impulse and Momentum56
- Ch 12: Rotation of a Rigid Body71
- Ch 13: Newton's Theory of Gravity52
- Ch 14: Fluids and Elasticity44
- Ch 15: Oscillations55
- Ch 16: Traveling Waves37
- Ch 17: Superposition39
- Ch 18: A Macroscopic Description of Matter53
- Ch 19: Work, Heat, and the First Law of Thermodynamics60
- Ch 20: The Micro/Macro Connection53
- Ch 21: Heat Engines and Refrigerators34
- Ch 22: Electric Charges and Forces40
- Ch 23: The Electric Field39
- Ch 24: Gauss' Law32
- Ch 25: The Electric Potential63
- Ch 26: Potential and Field57
- Ch 27: Current and Resistance42
- Ch 28: Fundamentals of Circuits39
- Ch 29: The Magnetic Field47
- Ch 30: Electromagnetic Induction60
- Ch 31: Electromagnetic Fields and Waves32
- Ch 32: AC Circuits63
- Ch 33: Wave Optics32
- Ch 34: Ray Optics57
- Ch 35: Optical Instruments30
- Ch 36: Special Relativity38
- Ch 37: The Foundations of Modern Physics25
- Ch 38: Quantization49
- Ch 39: Wave Functions and Uncertainty31
- Ch 40: One-Dimensional Quantum Mechanics35
- Ch 41: Atomic Physics18
- Ch 42: Nuclear Physics27
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Capitolo 39, Problema 8
In one experiment, 2000 photons are detected in a 0.10-mm-wide strip where the amplitude of the electromagnetic wave is 10 V/m. How many photons are detected in a nearby 0.10-mm-wide strip where the amplitude is 30 V/m?
Guida verificata passo dopo passo1
Understand that the number of photons detected is proportional to the intensity of the electromagnetic wave, and the intensity is proportional to the square of the amplitude of the wave. This means \( I \propto A^2 \), where \( I \) is the intensity and \( A \) is the amplitude.
Write the relationship between the number of photons detected \( N \) and the amplitude \( A \): \( N \propto A^2 \). This implies \( \frac{N_2}{N_1} = \frac{A_2^2}{A_1^2} \), where \( N_1 \) and \( N_2 \) are the number of photons detected in the first and second strips, and \( A_1 \) and \( A_2 \) are their respective amplitudes.
Substitute the given values for \( A_1 \) and \( A_2 \): \( A_1 = 10 \, \text{V/m} \) and \( A_2 = 30 \, \text{V/m} \). The equation becomes \( \frac{N_2}{N_1} = \frac{(30)^2}{(10)^2} \).
Simplify the ratio: \( \frac{N_2}{N_1} = \frac{900}{100} = 9 \). This means the number of photons detected in the second strip is 9 times the number detected in the first strip.
Multiply the number of photons detected in the first strip by this ratio to find \( N_2 \): \( N_2 = 9 \times 2000 \). This gives the number of photons detected in the second strip.
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Concetti chiave
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Photon Detection
Photon detection refers to the process of identifying and counting individual photons, which are the fundamental particles of light. The number of detected photons can be influenced by factors such as the intensity of the light source and the area over which the detection occurs. In this context, the experiment measures how varying the amplitude of the electromagnetic wave affects the number of photons detected in a specified area.
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Percorso guidato
07:11
Intensity of EM Waves Example 2
Amplitude of Electromagnetic Waves
The amplitude of an electromagnetic wave is a measure of the maximum electric field strength of the wave. It is directly related to the intensity of the wave, which is proportional to the square of the amplitude. Higher amplitude indicates a stronger wave, which can lead to a greater number of photons being emitted or detected, as seen in the comparison between the two strips in the experiment.
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Percorso guidato
05:22Introduction to Electromagnetic (EM) Waves
Intensity and Photon Flux
Intensity in the context of electromagnetic waves is defined as the power per unit area and is proportional to the square of the amplitude. Photon flux, which is the number of photons passing through a unit area per unit time, increases with higher intensity. Therefore, by understanding the relationship between intensity, amplitude, and photon detection, one can calculate the expected number of photons detected in different conditions.
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02:32Wave Intensity
Pratica correlata
Domanda del libro di testo
FIGURE EX39.13 shows the probability density for an electron that has passed through an experimental apparatus. What is the probability that the electron will land in a 0.010-mm-wide strip at x = 0.000 mm?
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Domanda del libro di testo
When 5×1012 photons pass through an experimental apparatus, 2.0×109 land in a 0.10-mm-wide strip. What is the probability density at this point?
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Domanda del libro di testo
FIGURE EX39.12 shows the probability density for an electron that has passed through an experimental apparatus. If 1.0×106 electrons are used, what is the expected number that will land in a 0.010-mm-wide strip at 2.000 mm?
103
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