Textbook Question
(b) Calculate the energy of a photon of radiation whose wavelength is 413 nm.
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Ch.6 - Electronic Structure of Atoms
Brown15th EditionChemistry: The Central ScienceISBN: 9780137542970
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Table of contents
- Ch.1 - Introduction: Matter, Energy, and Measurement146
- Ch.2 - Atoms, Molecules, and Ions200
- Ch.3 - Chemical Reactions and Reaction Stoichiometry176
- Ch.4 - Reactions in Aqueous Solution155
- Ch.5 - Thermochemistry126
- Ch.6 - Electronic Structure of Atoms131
- Ch.7 - Periodic Properties of the Elements126
- Ch.8 - Basic Concepts of Chemical Bonding123
- Ch.9 - Molecular Geometry and Bonding Theories143
- Ch.10 - Gases147
- Ch.11 - Liquids and Intermolecular Forces91
- Ch.12 - Solids and Modern Materials122
- Ch.13 - Properties of Solutions126
- Ch.14 - Chemical Kinetics174
- Ch.15 - Chemical Equilibrium101
- Ch.16 - Acid-Base Equilibria139
- Ch.17 - Additional Aspects of Aqueous Equilibria146
- Ch.18 - Chemistry of the Environment72
- Ch.19 - Chemical Thermodynamics129
- Ch.20 - Electrochemistry142
- Ch.21 - Nuclear Chemistry101
- Ch.22 - Chemistry of the Nonmetals68
- Ch.23 - Transition Metals and Coordination Chemistry66
- Ch.24 - The Chemistry of Life: Organic and Biological Chemistry10
Brown15th EditionChemistry: The Central ScienceISBN: 9780137542970Not the one you use?Change textbook
Chapter 6, Problem 25a
(a) Calculate the energy of a photon of electromagnetic radiation whose frequency is 2.94 × 1014 s-1.
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Identify the given frequency of the electromagnetic radiation, which is \(2.94 \times 10^{14} \, \text{s}^{-1}\).
Recall the formula for the energy of a photon, which is given by Planck's equation: \(E = h \nu\), where \(E\) is the energy of the photon, \(h\) is Planck's constant (\(6.626 \times 10^{-34} \, \text{J} \cdot \text{s}\)), and \(\nu\) is the frequency of the radiation.
Substitute the given frequency and the value of Planck's constant into the equation.
Perform the multiplication to calculate the energy in joules (J).
Interpret the result, understanding that the energy calculated represents the energy carried by a single photon of the given electromagnetic radiation.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Photon Energy
The energy of a photon is directly proportional to its frequency and can be calculated using the equation E = hν, where E is energy, h is Planck's constant (6.626 x 10^-34 J·s), and ν is the frequency in hertz. This relationship shows that higher frequency photons carry more energy.
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Photon Energy Formulas
Planck's Constant
Planck's constant is a fundamental constant in quantum mechanics that relates the energy of a photon to its frequency. It is a key component in the equation E = hν, and its value is approximately 6.626 x 10^-34 J·s. Understanding this constant is essential for calculating photon energy.
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Frequency of Electromagnetic Radiation
Frequency refers to the number of cycles of a wave that pass a point in one second, measured in hertz (Hz). In the context of electromagnetic radiation, frequency is inversely related to wavelength, and it plays a crucial role in determining the energy of the photon, as described by the equation E = hν.
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Related Practice
Textbook Question
If human height were quantized in 1-foot increments, what would happen to the height of a child as she grew up?
a. The child’s height would never change.
b. The child’s height would continuously get greater.
c. The child’s height would increase in “jumps” of 1 foot at a time.
d. The child’s height would increase in jumps of 6 inches.
Textbook Question
A laser pointer used in a lecture hall emits light at 650 nm. Using Figure 6.4, predict the color associated with this wavelength.
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Textbook Question
It is possible to convert radiant energy into electrical energy using photovoltaic cells. Assuming equal efficiency of conversion, would infrared or ultraviolet radiation yield more electrical energy on a per-photon basis?
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Textbook Question
(b) What is the energy of one of these photons?
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Textbook Question
(a) A green laser pointer emits light with a wavelength of 532 nm. What is the frequency of this light?