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?

Understanding the energy of a photon is crucial when discussing laser efficiency. The photon energy formula is a fundamental expression given by the equation: \[\begin{equation}E = \frac{hc}{\lambda} \text{,}\end{equation}\]where \(E\) represents the energy of a photon, \(h\) is Planck's constant, \(c\) is the speed of light, and \(\lambda\) is the wavelength of the photon. This equation helps us determine how much energy each photon carries based on its wavelength. Specifically, shorter wavelengths correspond to higher energy photons, which is an integral concept in applications like lasers. In our laser efficiency problem, this formula is the first step to calculating the total light-energy output.

Planck's constant, denoted as \(h\), is a crucial component in quantum mechanics and holds the value of approximately \(6.626 \times 10^{-34}\) joule-seconds (J·s). It relates the energy of light quanta, or photons, to their frequency and was first introduced by Max Planck. This constant is a cornerstone of the photon energy formula and is necessary for calculating the energy associated with a photon. When working with laser efficiency, Planck’s constant allows us to precisely determine the energy of each photon emitted by the laser.

The wavelength of a photon, represented by \(\lambda\), is the distance between successive peaks of its electromagnetic wave. It is inversely related to the photon's energy: the shorter the wavelength, the more energy the photon carries. In our exercise, the wavelength given for the laser's photons is 1064 nm (nanometers), which needs to be converted to meters (by multiplying by \(10^{-9}\)) when using the photon energy formula. Understanding the relationship between wavelength and energy helps explain why lasers with different colors (wavelengths) have varied applications.

The light-energy output of a laser refers to the total energy carried by the photons it emits. It can be calculated by determining the energy of a single photon and multiplying by the number of photons emitted per second. This figure is crucial for calculating the efficiency of a laser, as it directly compares the energy put into the laser in the form of electricity with the usable light energy it produces. In practical terms, a laser with a higher light-energy output will be more powerful, assuming the electrical power input remains constant.

The electrical power input is the amount of electrical energy supplied to the laser per second, measured in watts (W) where 1 watt equals 1 joule per second. This input energy is necessary for the laser to produce photons. When assessing laser efficiency, it's important to consider how much of this electrical power is successfully converted into light (the light-energy output). In the given exercise, the laser consumes 150.0 watts of electrical power, which sets the baseline for evaluating its efficiency.