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Ch.8 - The Quantum-Mechanical Model of the Atom
Tro - Chemistry: A Molecular Approach 5th Edition
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Tutti i libri di testoTro 5th EditionCh.8 - The Quantum-Mechanical Model of the AtomProblema 92
Capitolo 8, Problema 92

A particular laser consumes 150.0 watts of electrical power and produces a stream of 1.33×1019 1064-nm photons per second. What is the percent efficiency of the laser in converting electrical power to light?

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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 \( 1064 \times 10^{-9} \text{ m} \).
Determine the total energy of the photons produced per second by multiplying the energy of a single photon by the number of photons: \( E_{\text{total}} = E \times 1.33 \times 10^{19} \).
Convert the electrical power consumed by the laser from watts to joules per second, noting that 1 watt = 1 joule/second.
Calculate the efficiency of the laser by dividing the total energy of the photons produced per second by the electrical power consumed, and then multiply by 100 to express it as a percentage.
Express the final result as the percent efficiency of the laser in converting electrical power to light.

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Photon Energy

The energy of a photon is determined by its wavelength, which can be calculated using 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. For 1064-nm photons, this relationship allows us to find the energy per photon, which is essential for determining the total energy output of the laser.
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Photon Energy Formulas

Power and Energy Conversion

Power is defined as the rate at which energy is used or produced, measured in watts (W). In this context, the laser's power consumption (150.0 W) represents the electrical energy input, while the total energy output can be calculated by multiplying the number of photons produced per second by the energy per photon. This comparison is crucial for calculating efficiency.
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Conversion Factors

Efficiency Calculation

Efficiency is a measure of how effectively a system converts input energy into useful output energy, expressed as a percentage. It is calculated using the formula: Efficiency = (Output Power / Input Power) × 100%. In this case, the output power is the total energy produced by the photons per second, and the input power is the electrical power consumed by the laser.
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Stoichiometric Rate Calculations
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