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 6a
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?
Verified step by step guidance1
Determine the energy of the incident photons using the equation for photon energy: \( E = \frac{hc}{\lambda} \), where \( h \) is Planck's constant (\( 6.626 \times 10^{-34} \, \text{J·s} \)), \( c \) is the speed of light (\( 3.00 \times 10^8 \, \text{m/s} \)), and \( \lambda \) is the wavelength of the light (200 nm, converted to meters as \( 200 \times 10^{-9} \)).
Convert the photon energy from joules to electron volts (eV) using the conversion factor \( 1 \text{ eV} = 1.602 \times 10^{-19} \, \text{J} \).
Relate the stopping potential \( V_s \) to the maximum kinetic energy of the ejected electrons using the equation \( K_{\text{max}} = eV_s \), where \( e \) is the elementary charge (\( 1.602 \times 10^{-19} \, \text{C} \)) and \( V_s = 1.56 \, \text{V} \).
Use the photoelectric equation \( E = \phi + K_{\text{max}} \), where \( \phi \) is the work function of the metal, \( E \) is the photon energy, and \( K_{\text{max}} \) is the maximum kinetic energy of the ejected electrons. Rearrange to solve for \( \phi \): \( \phi = E - K_{\text{max}} \).
Compare the calculated work function \( \phi \) (in eV) to known work functions of metals to identify the material of the cathode.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Photoelectric Effect
The photoelectric effect is the phenomenon where electrons are emitted from a material (usually a metal) when it absorbs light of sufficient energy. This effect demonstrates the particle nature of light, as photons must have a minimum energy, known as the work function, to dislodge electrons from the material.
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The Doppler Effect
Stopping Potential
Stopping potential is the minimum voltage needed to stop the flow of photoelectrons emitted from a cathode in a photoelectric experiment. It is directly related to the kinetic energy of the emitted electrons, which can be calculated using the equation eV = KE, where e is the charge of the electron, V is the stopping potential, and KE is the kinetic energy of the electrons.
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Work Function
The work function is the minimum energy required to remove an electron from the surface of a metal. It is a characteristic property of each metal and is crucial in determining whether the energy of incoming photons (from light) is sufficient to overcome this barrier, thus allowing the photoelectric effect to occur.
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Related Practice
Textbook Question
Photoelectrons are observed when a metal is illuminated by light with a wavelength less than 388 nm. What is the metal's work function?
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Textbook Question
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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Textbook Question
Electrons in a photoelectric-effect experiment emerge from an aluminum surface with a maximum kinetic energy of 1.30 eV. What is the wavelength of the light?
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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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