Question

Which type of electromagnetic radiation has a wavelength roughly on the order of the height of a person? What can you say about the energy of this radiation?

Short answer

The type of electromagnetic radiation with a wavelength roughly on the order of the height of a person (1.7 meters) is VHF radio waves. The energy of this radiation is approximately \(1.17 \times 10^{-7}\) Joules, which is relatively low compared to other types of electromagnetic radiation.

Step-by-step solution

Identify the average height of a person

The height of a person can vary significantly, but we will assume an average height of about 1.7 meters (170 cm) for this problem.

Review the electromagnetic spectrum

The electromagnetic spectrum is divided into different types of radiation, with each type characterized by its wavelength. The main types of electromagnetic waves, in order from longest to shortest wavelength, are: 1. Radio waves 2. Microwaves 3. Infrared 4. Visible light 5. Ultraviolet 6. X-rays 7. Gamma rays We need to find which type of radiation has a wavelength close to 1.7 meters or 170 cm.

Identify the radiation type with a wavelength similar to a person's height

After reviewing the types of radiation, it appears that radio waves have wavelengths comparable to a person's height. More specifically, VHF (Very High Frequency) radio waves have wavelengths ranging from about 1 meter to 10 meters. The wavelength of 1.7 meters falls within this range.

Analyze the energy of the VHF radio waves

We can calculate the energy of the VHF radio waves using the following equation: Energy (E) = Planck's constant (h) × Speed of light (c) / Wavelength (λ) Planck's constant (h) = 6.63 × 10^{-34} Js Speed of light (c) = 3 × 10^8 m/s Wavelength (λ) = 1.7 m Now, we can plug in the values to find the energy of the VHF radio waves: E = (6.63 × 10^{-34} Js) × (3 × 10^8 m/s) / (1.7 m) E ≈ 1.17 × 10^{-7} J

Conclusion

The type of electromagnetic radiation with a wavelength roughly on the order of the height of a person (1.7 meters) is VHF radio waves. The energy of this radiation is approximately 1.17 × 10^{-7} Joules, which is relatively low compared to other types of electromagnetic radiation.

Key concepts

VHF Radio Waves

The fascinating world of electromagnetic spectrum brings us a variety of different types of radiation, one of which is the Very High Frequency (VHF) radio waves. VHF radio waves lie within the frequency range of 30 to 300 MHz, which corresponds to wavelengths from about 10 meters to 1 meter. This range is particularly significant in communication as it's used for television broadcasts, FM radio, and other forms of communication, including some emergency services and amateur radio.

VHF's ability to penetrate through the atmosphere makes it suitable for long-distance terrestrial communication, and because of its longer wavelengths, VHF waves can travel further beyond the horizon compared to higher frequency waves. However, they are still susceptible to interference by buildings and natural terrain, which can affect their propagation.

Wavelength

Wavelength can be simply thought of as the distance between successive crests of a wave. In the case of electromagnetic radiation, it is typically measured in meters, centimeters, or nanometers, depending on the part of the spectrum being considered. The wavelength is inversely proportional to the frequency of the wave; as the frequency increases, the wavelength decreases, and vice versa.

In the context of our earlier exercise, we focused on a wavelength of approximately 1.7 meters, which correlates to myriads of things around us, such as the height of an average human. In relation to the electromagnetic spectrum, a wavelength of 1.7 meters falls within the VHF radio band. Understanding the concept of wavelength is crucial for a wide range of applications, from tuning your radio to the right station to characterizing different forms of light and other types of electromagnetic radiation.

Planck's Constant

Fundamental to the understanding of quantum mechanics, Planck's Constant (\( h \)) is a physical constant that relates the energy of a photon to its frequency (\( f \)). Discovered by Max Planck, this constant has a value of approximately 6.62607015 × 10^{-34} joule-seconds. The formula to connect energy and frequency using Planck's constant is given by:\begin{nmath} E = h \times f {math}This equation can also be manipulated to link the energy of a photon with its wavelength (\( u \)) by incorporating the speed of light (\( c \)), since frequency multiplied by wavelength equals the speed of light in a vacuum. Thus, the relation becomes\begin{nmath} E = \frac{h \times c}{u} {math}Recognizing the significance of Planck's constant is vital because it enables us to calculate the precise quanta of energy carried by photons, which is instrumental in technologies such as LEDs, lasers, and even the understanding of the chemical bonds that hold molecules together.