Domanda del libro di testo
One type of sunburn occurs on exposure to UV light of wavelength in the vicinity of 325 nm. (a) What is the energy of a photon of this wavelength?
Ch.6 - Electronic Structure of Atoms
Brown14th EditionChemistry: The Central ScienceISBN: 9780134414232
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TOC.tableOfContents
- Ch.1 - Introduction: Matter, Energy, and Measurement177
- Ch.2 - Atoms, Molecules, and Ions231
- Ch.3 - Chemical Reactions and Reaction Stoichiometry216
- Ch.4 - Reactions in Aqueous Solution189
- Ch.5 - Thermochemistry175
- Ch.6 - Electronic Structure of Atoms168
- Ch.7 - Periodic Properties of the Elements150
- Ch.8 - Basic Concepts of Chemical Bonding177
- Ch.9 - Molecular Geometry and Bonding Theories200
- Ch.10 - Gases179
- Ch.11 - Liquids and Intermolecular Forces113
- Ch.12 - Solids and Modern Materials154
- Ch.13 - Properties of Solutions157
- Ch.14 - Chemical Kinetics199
- Ch.15 - Chemical Equilibrium128
- Ch.16 - Acid-Base Equilibria164
- Ch.17 - Additional Aspects of Aqueous Equilibria163
- Ch.18 - Chemistry of the Environment105
- Ch.19 - Chemical Thermodynamics164
- Ch.20 - Electrochemistry171
- Ch.21 - Nuclear Chemistry122
- Ch.22 - Chemistry of the Nonmetals82
- Ch.23 - Transition Metals and Coordination Chemistry79
- Ch.24 - The Chemistry of Life: Organic and Biological Chemistry16
Brown14th EditionChemistry: The Central ScienceISBN: 9780134414232Non è quello che usi tu?Cambia libro di testo
Capitolo 6, Problema 29c
One type of sunburn occurs on exposure to UV light of wavelength in the vicinity of 325 nm. (c) How many photons are in a 1.00 mJ burst of this radiation?
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Convert the energy of the burst from millijoules to joules. Remember that 1 mJ = 0.001 J.
Calculate the energy of a single photon using the formula: \( E = \frac{hc}{\lambda} \), where \( h \) 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 in meters (325 nm = 325 \(\times\) 10^{-9} \(\text{ m}\)).
Determine the number of photons by dividing the total energy of the burst by the energy of a single photon: \( \text{Number of photons} = \frac{\text{Total energy}}{\text{Energy per photon}} \).
Ensure all units are consistent, particularly energy in joules and wavelength in meters, to maintain dimensional accuracy.
Perform the division to find the number of photons, ensuring to keep track of significant figures based on the given data.
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Photon Energy
The energy of a photon is determined by its wavelength and can be calculated using the equation E = hc/λ, where E is energy, h is Planck's constant (6.626 x 10^-34 J·s), c is the speed of light (3.00 x 10^8 m/s), and λ is the wavelength in meters. For UV light at 325 nm, this relationship allows us to find the energy of a single photon.
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01:40
Photon Energy Formulas
Conversion of Units
In chemistry, it is essential to convert units appropriately to ensure consistency in calculations. In this case, the energy burst of 1.00 mJ must be converted to joules (1 mJ = 0.001 J) to match the units used in the photon energy equation. This step is crucial for accurately determining the number of photons in the given energy burst.
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01:56Conversion Factors
Calculating Number of Photons
To find the number of photons in a given energy burst, divide the total energy by the energy of a single photon. This is expressed mathematically as N = E_total / E_photon, where N is the number of photons, E_total is the total energy in joules, and E_photon is the energy of one photon calculated from its wavelength. This calculation provides insight into the quantized nature of light.
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01:22Calculate Oxidation Numbers Example
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One type of sunburn occurs on exposure to UV light of wavelength in the vicinity of 325 nm. (d) These UV photons can break chemical bonds in your skin to cause sunburn—a form of radiation damage. If the 325-nm radiation provides exactly the energy to break an average chemical bond in the skin, estimate the average energy of these bonds in kJ/mol.
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