Skip to main content
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 100
Capitolo 8, Problema 100

A particular laser consumes 140.0 watts of electrical power and produces a stream of 1.25×1019 1064-nm photons per second. What is the percent efficiency of the laser in converting electrical power to light?

Guida verificata passo dopo passo
1
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: \( E_{\text{total}} = E \times 1.25 \times 10^{19} \).
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.
Summarize the steps to ensure understanding: calculate photon energy, total photon energy per second, convert power units, and find efficiency percentage.

Risposta video verificata per un problema simile:

Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.
Durata del video:
4m

Concetti chiave

Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.

Photon Energy

The energy of a photon is determined by its wavelength, given by 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 1064 nm (1.064 x 10^-6 m), this relationship allows us to calculate the energy of each photon emitted by the laser.
Video consigliato:
Percorso guidato
01:40
Photon Energy Formulas

Power and Energy Conversion

Power is the rate at which energy is used or produced, measured in watts (W), where 1 W = 1 J/s. In this context, the laser's power consumption (140.0 W) indicates how much electrical energy is being converted into light energy per second. To find efficiency, we compare the useful output energy (light) to the input energy (electricity).
Video consigliato:
Percorso guidato
01:56
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 (%) = (Useful Output Energy / Input Energy) × 100. In this case, we will calculate the total energy output from the emitted photons and compare it to the electrical power consumed by the laser to determine its efficiency.
Video consigliato:
Percorso guidato
02:28
Stoichiometric Rate Calculations
Pratica correlata
Domanda del libro di testo

The distance from Earth to the sun is 1.5×108 km. Find the number of crests in a light wave of frequency 1.0×1014 s –1 traveling from the sun to Earth.

2153
views
1
rank
Domanda del libro di testo

A 5.00-mL ampule of a 0.100-M solution of naphthalene in hexane is excited with a flash of light. The naphthalene emits 12.3 J of energy at an average wavelength of 349 nm. What percentage of the naphthalene molecules emitted a photon?

Domanda del libro di testo

A laser produces 20.0 mW of red light. In 30.0 minutes, the laser emits 1.15×1020 photons. What is the wavelength of the laser?