Textbook Question
What is the wavelength, in nm, of a photon with energy (a) 0.30 eV, (b) 3.0 eV, and (c) 30 eV? For each, is this wavelength visible, ultraviolet, or infrared light?
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Ch 38: Quantization
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796
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Table of contents
- 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
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook
Chapter 38, Problem 14
What is the energy, in keV, of 75 keV x-ray photons that are backscattered (i.e., scattered directly back toward the source) by the electrons in a target?
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Understand the problem: The energy of the backscattered photon can be determined using the Compton scattering formula. This involves the relationship between the initial photon energy, the scattering angle (180° for backscattering), and the energy of the scattered photon.
Write the Compton wavelength shift formula: Δλ = λ' - λ = (h / (m_e * c)) * (1 - cos(θ)), where h is Planck's constant, m_e is the electron mass, c is the speed of light, λ is the initial wavelength, λ' is the scattered wavelength, and θ is the scattering angle (180° for backscattering).
Relate the wavelength to energy: Use the formula E = h * c / λ to express the initial and scattered photon energies in terms of their respective wavelengths. The initial energy is given as 75 keV, so calculate the initial wavelength λ using this formula.
Substitute the values into the Compton formula: Use the known constants (h, m_e, c) and the scattering angle θ = 180° to calculate the wavelength shift Δλ. Then, find the scattered wavelength λ' by adding Δλ to the initial wavelength λ.
Determine the energy of the backscattered photon: Use the formula E' = h * c / λ' to calculate the energy of the scattered photon in keV. This will give the energy of the backscattered photon.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Photon Energy
Photon energy is defined by the equation E = hf, where E is energy, h is Planck's constant, and f is the frequency of the photon. In the context of x-rays, the energy is often expressed in electronvolts (eV) or kiloelectronvolts (keV), with 1 keV equal to 1,000 eV. Understanding photon energy is crucial for analyzing interactions between photons and matter.
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Intro to Energy & Types of Energy
Backscattering
Backscattering refers to the phenomenon where particles, such as photons or electrons, are deflected back toward their source after colliding with a target. In the case of x-ray photons, backscattering can occur when photons interact with electrons in a material, leading to a change in direction and energy. This concept is important for understanding how x-rays interact with matter and the implications for imaging and radiation therapy.
Compton Scattering
Compton scattering is a specific type of scattering that occurs when x-ray or gamma-ray photons collide with electrons, resulting in a transfer of energy and a change in the direction of the photon. This interaction is characterized by a decrease in the energy of the photon and an increase in the kinetic energy of the electron. Compton scattering is significant in medical imaging and radiation physics, as it affects the energy and intensity of x-ray beams.
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Related Practice
Textbook Question
At what speed is an electron’s de Broglie wavelength (a) 1.0 nm, (b) 1.0 μm, and (c) 1.0 mm?
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Textbook Question
A photoelectric-effect experiment finds a stopping potential of 1.56 V when light of 200 nm is used to illuminate the cathode. From what metal is the cathode made?
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Textbook Question
INT Through what potential difference must an electron be accelerated from rest to have a de Broglie wavelength of 500 nm?
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Textbook Question
A 100 W incandescent lightbulb emits about 5 W of visible light. (The other 95 W are emitted as infrared radiation or lost as heat to the surroundings.) The average wavelength of the visible light is about 600 nm, so make the simplifying assumption that all the light has this wavelength. How many visible-light photons does the bulb emit per second?
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Textbook Question
55 keV x-ray photons are incident on a target. At what scattering angle do the scattered photons have an energy of 50 keV?
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