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?

검증된 단계별 안내

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.

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주요 개념

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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.

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).

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.

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?