Textbook Question
The H2 molecule has a moment of inertia of kg-m2. What is the wavelength of the photon absorbed when H2 makes a transition from the to the rotational level?
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Ch 42: Molecules and Condensed Matter
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552
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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
Chapter 41, Problem 2a
During each of these processes, a photon of light is given up. In each process, what wavelength of light is given up, and in what part of the electromagnetic spectrum is that wavelength? A molecule decreases its vibrational energy by eV.
Verified step by step guidance1
Step 1: Understand the relationship between energy and wavelength using the equation \( E = \frac{hc}{\lambda} \), where \( E \) is the energy of the photon, \( h \) 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.
Step 2: Convert the energy given in electron volts (eV) to joules (J). Use the conversion factor \( 1 \text{ eV} = 1.602 \times 10^{-19} \, \text{J} \). Multiply \( 0.198 \, \text{eV} \) by \( 1.602 \times 10^{-19} \, \text{J/eV} \) to find the energy in joules.
Step 3: Rearrange the equation \( E = \frac{hc}{\lambda} \) to solve for wavelength \( \lambda \): \( \lambda = \frac{hc}{E} \). Substitute the values for \( h \), \( c \), and the energy \( E \) (converted to joules) into the equation.
Step 4: Calculate the wavelength \( \lambda \) in meters. If needed, convert the result to nanometers (nm) by multiplying the value in meters by \( 10^9 \).
Step 5: Determine the part of the electromagnetic spectrum the wavelength belongs to by comparing the calculated wavelength to the ranges of the spectrum (e.g., infrared, visible, ultraviolet). For reference, visible light ranges from approximately 400 nm to 700 nm, while infrared is longer than 700 nm.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Photon Energy and Wavelength
The energy of a photon is inversely related to its wavelength, described by the equation E = hc/λ, where E is energy, h is Planck's constant, c is the speed of light, and λ is the wavelength. A decrease in vibrational energy of a molecule corresponds to the emission of a photon with a specific wavelength, which can be calculated using this relationship.
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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. The visible spectrum, which is a small part of the electromagnetic spectrum, includes wavelengths from approximately 400 nm (violet) to 700 nm (red).
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Energy Units and Conversion
Energy in physics is often measured in electronvolts (eV), a unit commonly used in atomic and particle physics. To find the corresponding wavelength of light emitted when a molecule loses energy, one must convert the energy from eV to joules (1 eV = 1.602 x 10^-19 joules) and then use the photon energy-wavelength relationship to determine the wavelength in meters or nanometers.
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Related Practice
Textbook Question
Two atoms of cesium (Cs) can form a molecule. The equilibrium distance between the nuclei in a molecule is nm. Calculate the moment of inertia about an axis through the center of mass of the two nuclei and perpendicular to the line joining them. The mass of a cesium atom is kg.
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Textbook Question
For the H2 molecule the equilibrium spacing of the two protons is nm. The mass of a hydrogen atom is kg. Calculate the wavelength of the photon emitted in the rotational transition to .
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