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 5a
Young & Freedman Calc 14th EditionCh 38: Photons: Light Waves Behaving as ParticlesProblem 5aChapter 38, Problem 5a
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.
Verified step by step guidance1
Step 1: Recall the relationship between the energy \(E\) of a photon and its momentum \(p\). The formula is \(E = pc\), where \(c\) is the speed of light in a vacuum (\(c = 3.00 \times 10^8\, \text{m/s}\)).
Step 2: Substitute the given momentum \(p = 8.24 \times 10^{-28}\, \text{kg·m/s}\) and the speed of light \(c = 3.00 \times 10^8\, \text{m/s}\) into the formula \(E = pc\). This will give the energy in joules.
Step 3: To convert the energy from joules to electron volts (eV), use the conversion factor \(1\, \text{eV} = 1.602 \times 10^{-19}\, \text{J}\). Divide the energy in joules by this factor to find the energy in electron volts.
Step 4: Ensure that the units are consistent throughout the calculation. Verify that the energy in joules and electron volts are correctly calculated and match the expected order of magnitude.
Step 5: Present the final energy values in both joules and electron volts, ensuring proper significant figures based on the given data.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Photon Momentum
Photons, which are particles of light, possess momentum despite having no mass. The momentum of a photon is given by the equation p = E/c, where p is momentum, E is energy, and c is the speed of light in a vacuum. 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
Energy of a Photon
The energy of a photon can be calculated using the equation E = hf, where E is energy, h is Planck's constant (approximately 6.626 x 10^-34 J·s), and f is the frequency of the photon. Alternatively, energy can also be expressed in terms of momentum using E = pc, linking the concepts of energy and momentum for massless particles like photons.
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Conversion Between Joules and Electron Volts
Energy can be expressed in different units, with joules (J) and electron volts (eV) being common in physics. One electron volt is defined as the energy gained by an electron when it is accelerated through a potential difference of one volt, equivalent to approximately 1.602 x 10^-19 joules. Understanding how to convert between these units is essential for accurately reporting energy values in various contexts.
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Related Practice
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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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 wavelength of this photon? In what region of the electromagnetic spectrum does it lie?
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