Textbook Question
A photon of green light has a wavelength of nm. Find the photon's frequency, magnitude of momentum, and energy. Express the energy in both joules and electron volts.
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Ch 38: Photons: Light Waves Behaving as Particles
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610
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Table of contents
- Ch 01: Units, Physical Quantities & Vectors41
- Ch 02: Motion Along a Straight Line67
- Ch 03: Motion in Two or Three Dimensions47
- Ch 04: Newton's Laws of Motion23
- Ch 05: Applying Newton's Laws59
- Ch 06: Work & Kinetic Energy14
- Ch 07: Potential Energy & Conservation8
- Ch 08: Momentum, Impulse, and Collisions18
- Ch 09: Rotation of Rigid Bodies42
- Ch 10: Dynamics of Rotational Motion48
- Ch 11: Equilibrium & Elasticity27
- Ch 12: Fluid Mechanics31
- Ch 13: Gravitation35
- Ch 14: Periodic Motion32
- Ch 15: Mechanical Waves25
- Ch 16: Sound & Hearing32
- Ch 17: Temperature and Heat36
- Ch 18: Thermal Properties of Matter38
- Ch 19: The First Law of Thermodynamics33
- Ch 20: The Second Law of Thermodynamics22
- Ch 21: Electric Charge and Electric Field36
- Ch 22: Gauss' Law24
- Ch 23: Electric Potential31
- Ch 24: Capacitance and Dielectrics18
- Ch 25: Current, Resistance, and EMF26
- Ch 26: Direct-Current Circuits30
- Ch 27: Magnetic Field and Magnetic Forces18
- Ch 28: Sources of Magnetic Field10
- Ch 29: Electromagnetic Induction28
- Ch 30: Inductance17
- Ch 31: Alternating Current21
- Ch 32: Electromagnetic Waves1
- Ch 33: The Nature and Propagation of Light20
- Ch 34: Geometric Optics34
- Ch 35: Interference19
- Ch 36: Diffraction25
- Ch 37: Special Relativity20
- Ch 38: Photons: Light Waves Behaving as Particles15
- Ch 39: Particles Behaving as Waves26
- Ch 40: Quantum Mechanics I: Wave Functions21
- Ch 41: Quantum Mechanics II: Atomic Structure25
- Ch 42: Molecules and Condensed Matter18
- Ch 43: Nuclear Physics16
- Ch 44: Particle Physics and Cosmology23
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Not the one you use?Change textbook
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Young & Freedman Calc 14th EditionCh 38: Photons: Light Waves Behaving as ParticlesProblem 5b
Young & Freedman Calc 14th EditionCh 38: Photons: Light Waves Behaving as ParticlesProblem 5bChapter 38, Problem 5b
A photon has momentum of magnitude kg-m/s. What is the wavelength of this photon? In what region of the electromagnetic spectrum does it lie?
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Step 1: Recall the relationship between the momentum of a photon and its wavelength. The equation is given by \( p = \frac{h}{\lambda} \), where \( p \) is the momentum, \( h \) is Planck's constant (\( 6.626 \times 10^{-34} \, \text{J} \cdot \text{s} \)), and \( \lambda \) is the wavelength.
Step 2: Rearrange the equation to solve for the wavelength \( \lambda \). This gives \( \lambda = \frac{h}{p} \).
Step 3: Substitute the given values into the equation. The momentum \( p \) is \( 8.24 \times 10^{-28} \, \text{kg} \cdot \text{m/s} \), and \( h \) is \( 6.626 \times 10^{-34} \, \text{J} \cdot \text{s} \). Ensure the units are consistent.
Step 4: Perform the division \( \lambda = \frac{6.626 \times 10^{-34}}{8.24 \times 10^{-28}} \) to calculate the wavelength. This will yield the wavelength in meters.
Step 5: Determine the region of the electromagnetic spectrum by comparing the calculated wavelength to known ranges of wavelengths for different regions (e.g., gamma rays, X-rays, ultraviolet, visible light, infrared, microwaves, and radio waves).
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Photon Momentum
Photons, despite having no mass, carry momentum, which is given by the formula p = E/c, where p is momentum, E is energy, and c is the speed of light. This relationship highlights the wave-particle duality of light, where photons exhibit both wave-like and particle-like properties.
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Intro to Momentum
Wavelength and Frequency Relationship
The wavelength (λ) of a photon is inversely related to its frequency (ν) through the equation c = λν, where c is the speed of light. This means that as the wavelength increases, the frequency decreases, and vice versa, which is crucial for determining the characteristics of electromagnetic radiation.
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Electromagnetic Spectrum
The electromagnetic spectrum encompasses all types of electromagnetic radiation, ranging from radio waves to gamma rays. Each type of radiation is characterized by its wavelength and frequency, and the position of a photon within this spectrum determines its energy and potential applications in technology and science.
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Related Practice
Textbook Question
The photoelectric work function of potassium is eV. If light that has a wavelength of nm falls on potassium, find the stopping potential in volts.
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Textbook Question
The photoelectric threshold wavelength of a tungsten surface is nm. Calculate the maximum kinetic energy of the electrons ejected from this tungsten surface by ultraviolet radiation of frequency Hz. Express the answer in electron volts.
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Textbook Question
What would the minimum work function for a metal have to be for visible light (– nm) to eject photoelectrons?
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Textbook Question
A laser used to weld detached retinas emits light with a wavelength of nm in pulses that are ms in duration. The average power during each pulse is W. How much energy is in each pulse in joules? In electron volts?
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Textbook Question
A photon has momentum of magnitude kg-m/s. What is the energy of this photon? Give your answer in joules and in electron volts.
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