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.
4
views
Ch 38: Photons: Light Waves Behaving as Particles
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552
Not the one you use?Change textbookSelect a different textbook
Table of contents
- Ch 01: Units, Physical Quantities & Vectors37
- Ch 02: Motion Along a Straight Line57
- Ch 03: Motion in Two or Three Dimensions45
- Ch 04: Newton's Laws of Motion23
- Ch 05: Applying Newton's Laws54
- Ch 06: Work & Kinetic Energy11
- Ch 07: Potential Energy & Conservation6
- Ch 08: Momentum, Impulse, and Collisions15
- Ch 09: Rotation of Rigid Bodies37
- Ch 10: Dynamics of Rotational Motion44
- Ch 11: Equilibrium & Elasticity27
- Ch 12: Fluid Mechanics27
- Ch 13: Gravitation34
- Ch 14: Periodic Motion26
- Ch 15: Mechanical Waves22
- Ch 16: Sound & Hearing28
- Ch 17: Temperature and Heat28
- Ch 18: Thermal Properties of Matter35
- Ch 19: The First Law of Thermodynamics29
- Ch 20: The Second Law of Thermodynamics18
- Ch 21: Electric Charge and Electric Field28
- Ch 22: Gauss' Law21
- Ch 23: Electric Potential31
- Ch 24: Capacitance and Dielectrics18
- Ch 25: Current, Resistance, and EMF24
- Ch 26: Direct-Current Circuits29
- Ch 27: Magnetic Field and Magnetic Forces16
- Ch 28: Sources of Magnetic Field10
- Ch 29: Electromagnetic Induction22
- Ch 30: Inductance14
- Ch 31: Alternating Current20
- Ch 33: The Nature and Propagation of Light17
- Ch 34: Geometric Optics29
- Ch 35: Interference13
- Ch 36: Diffraction19
- Ch 37: Special Relativity19
- Ch 38: Photons: Light Waves Behaving as Particles12
- Ch 39: Particles Behaving as Waves25
- Ch 40: Quantum Mechanics I: Wave Functions20
- Ch 41: Quantum Mechanics II: Atomic Structure21
- Ch 42: Molecules and Condensed Matter17
- Ch 43: Nuclear Physics13
- Ch 44: Particle Physics and Cosmology17
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Not the one you use?Change textbook
All textbooks
Young & Freedman Calc 15th EditionCh 38: Photons: Light Waves Behaving as ParticlesProblem 5b
Young & Freedman Calc 15th EditionCh 38: Photons: Light Waves Behaving as ParticlesProblem 5bChapter 37, 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?
Verified step by step guidance1
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).
Verified video answer for a similar problem:
This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
3mWas this helpful?
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.
Recommended video:
Guided course
05:17
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.
Recommended video:
Guided course
05:08Circumference, Period, and Frequency in UCM
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.
Recommended video:
Guided course
06:06The Electromagnetic Spectrum
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.
3
views
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?
3
views
Textbook Question
The photoelectric work function of potassium is eV. If light that has a wavelength of nm falls on potassium, find the kinetic energy, in electron volts, of the most energetic electrons ejected.
3
views
Textbook Question
The cathode-ray tubes that generated the picture in early color televisions were sources of x rays. If the acceleration voltage in a television tube is kV, what are the shortest-wavelength x rays produced by the television?
4
views
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.
14
views