A diode laser emits at a wavelength of 987 \(\mathrm{nm}\) . (a) In what portion of the electromagnetic spectrum is this radiation found? (b) All of its output energy is absorbed in a detector that measures a total energy of 0.52 \(\mathrm{J}\) over a period of 32 s. How many photons per second are being emitted by the laser?

The electromagnetic (EM) spectrum encompasses all types of electromagnetic radiation, which varies in wavelength and frequency. This range includes, from shortest to longest wavelength: gamma rays, X-rays, ultraviolet rays, visible light, infrared radiation, microwaves, and radio waves. Wavelengths are typically measured in meters, with visible light wavelengths ranging from about 400 nm to 700 nm. As we move towards infrared, microwaves, and radio waves, the wavelengths get progressively longer, while gamma rays and X-rays have much shorter wavelengths.

This spectrum is fundamental to understanding how different types of electromagnetic waves interact with matter, as each category of wave has unique properties and applications. For instance, X-rays can penetrate soft tissues, making them invaluable in medical imaging, while radio waves are long enough to be used for broadcasting signals over large distances.

Infrared radiation is a type of electromagnetic radiation with wavelengths longer than visible light but shorter than microwaves, typically ranging from 700 nm to 1 mm. It is invisible to the human eye, but we can feel it as heat, which signifies how it transfers energy. Infrared is often divided into subcategories: near-infrared (closest to visible light), mid-infrared, and far-infrared (closest to microwaves).

Objects at room temperature emit infrared as thermal radiation. This property is harnessed in various technologies, such as night-vision equipment and thermal imaging, which detect infrared radiation from warm objects against cooler backgrounds. In the context of the exercise, infrared radiation is identified by the laser's wavelength of 987 nm, situating it in the infrared region of the spectrum.

Planck's equation, devised by physicist Max Planck, is a fundamental relationship in quantum mechanics connecting the energy of a photon to its frequency (or through the speed of light, its wavelength). The equation is expressed as: \[ E = h\frac{c}{\lambda} \] where \(E\) denotes the energy of the photon, \(h\) is Planck’s constant (approximately \(6.626 \times 10^{-34} Js\)), \(c\) is the speed of light in a vacuum (roughly \(3 \times 10^8 m/s\)), and \(\lambda\) is the wavelength of the photon.

Understanding this equation is crucial in fields such as quantum physics, chemistry, and astronomy because it bridges the gap between the macroscopic classical world and the microscopic quantum world. It indicates how the quantized nature of light can lead to phenomena like the photoelectric effect and plays a pivotal role in determining the characteristics of photons emitted or absorbed by atoms.

The energy of a photon is intrinsic to its identity in the quantum world. According to Planck's equation, the energy is directly proportional to its frequency and inversely proportional to its wavelength. This means that photons of light with higher frequencies (and thus shorter wavelengths) like gamma rays pack more energy than those with lower frequencies such as radio waves.

To compute the energy of a single photon in practical applications like our exercise, you'd rearrange Planck's equation to substitute for wavelength if the frequency is unknown. Given that the energy of each photon is quantized, when lasers or other light sources emit photons, each one carries a discrete 'packet' of energy. By knowing the energy of one photon and the total energy emitted or absorbed, as shown in the exercise solution, one can determine the quantity of photons involved in the process which is crucial for scientific experiments and industrial applications like laser technology.