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Ch.8 - The Quantum-Mechanical Model of the Atom
Tro - Chemistry: A Molecular Approach 6th Edition
Tro6th EditionChemistry: A Molecular ApproachISBN: 9780137832217Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoTro 6th EditionCh.8 - The Quantum-Mechanical Model of the AtomProblema 46
Capitolo 8, Problema 46

A heat lamp produces 17.7 watts of power at a wavelength of 6.5 μm. How many photons are emitted per second? (1 watt = 1 J/s)

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Identify the given values: power (P) = 17.7 watts, wavelength (\(\lambda\)) = 6.5 \(\mu\)m.
Convert the wavelength from micrometers to meters: \(\lambda = 6.5 \times 10^{-6}\) m.
Use the formula for energy of a photon: \(E = \frac{hc}{\lambda}\), where \(h\) is Planck's constant (\(6.626 \times 10^{-34}\) J\(\cdot\) s) and \(c\) is the speed of light (\(3.00 \times 10^8\) m/s).
Calculate the energy of a single photon using the converted wavelength.
Determine the number of photons emitted per second by dividing the total power by the energy of a single photon: \(\text{Number of photons} = \frac{P}{E}\).

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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. This relationship shows that shorter wavelengths correspond to higher energy photons.
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Photon Energy Formulas

Power and Energy Relationship

Power is defined as the rate at which energy is emitted or transferred, measured in watts (1 watt = 1 joule/second). In this context, the power of the heat lamp indicates how much energy is emitted per second, which is crucial for determining the number of photons emitted based on their individual energy.
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Power and Root Functions Example

Calculating Photon Emission

To find the number of photons emitted per second, divide the total power output of the lamp by the energy of a single photon. This calculation involves first determining the energy of a photon using its wavelength, and then using the formula: Number of photons = Power / Energy per photon, which provides the total count of photons emitted each second.
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Gamma Emission
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