Problem 18 - Chemistry: The Central Science in SI Units, Global Edition

Question

List the following types of electromagnetic radiation in order of descending wavelength: (a) UV lights used in tanning salons \((300-400 \mathrm{nm}) ;\) (b) radiation from an FM radio station at \(93.1 \mathrm{MHz}\) on the dial; (c) radiation from mobile phones \((450-2100 \mathrm{MHz}) ;\) (d) the yellow light from sodium vapor streetlights; (e) the red light of a light-emitting diode, such as in an appliance's display.

Step-by-Step Solution

Answer

The types of radiation in descending order of wavelengths are: 1. Radiation from an FM radio station at 93.1 MHz: 3.22 m 2. Radiation from mobile phones: 0.143 - 0.667 m 3. Red light from a LED: 620 - 750 nm (0.000620 - 0.000750 m) 4. Yellow light from sodium vapor streetlights: 570 - 590 nm (0.000570 - 0.000590 m) 5. UV lights used in tanning salons: 300 - 400 nm (0.000300 - 0.000400 m)

Step 1: Calculate the wavelengths for each type of radiation

(a) UV lights used in tanning salons (300-400 nm) - Already given in terms of wavelength. (b) Radiation from an FM radio station at 93.1 MHz - Convert frequency to wavelength: Wavelength = \(\frac{3 \times 10^8 m/s}{93.1 \times 10^6 Hz}\) = \(3.22 m\). (c) Radiation from mobile phones (450-2100 MHz) - Convert frequencies to wavelengths: Wavelength range = \(\frac{3 \times 10^8 m/s}{2100 \times 10^6 Hz}\) to \(\frac{3 \times 10^8 m/s}{450 \times 10^6 Hz} = 0.143 m - 0.667 m\). (d) The yellow light from sodium vapor streetlights: Yellow light has a wavelength range of approximately 570-590 nm. (e) The red light of a LED: Red light typically has a wavelength range of approximately 620-750 nm.

Step 2: Arrange the wavelengths in descending order

Now that we have the wavelengths for all types of radiation, we can list them in descending order: 1. Radiation from an FM radio station at 93.1 MHz: 3.22 m 2. Radiation from mobile phones: 0.143 - 0.667 m 3. Red light from a LED: 620 - 750 nm (0.000620 - 0.000750 m) 4. Yellow light from sodium vapor streetlights: 570 - 590 nm (0.000570 - 0.000590 m) 5. UV lights used in tanning salons: 300 - 400 nm (0.000300 - 0.000400 m) So, the types of radiation in descending order of wavelengths are: FM radio station, mobile phone radiation, LED red light, sodium vapor yellow light, and tanning salon UV light.

Key Concepts

Wavelength Calculation

Wavelength is a key property of electromagnetic radiation that tells us the distance between consecutive peaks of a wave. In the case of light and other forms of electromagnetic radiation, it is often measured in nanometers (nm) or meters (m). Understanding how to calculate the wavelength is crucial for distinguishing between different types of electromagnetic waves. When given the frequency of radiation, such as in FM radio waves, we utilize the formula:
\[ \text{Wavelength} = \frac{c}{\text{Frequency}} \] where

• \(c\) is the speed of light, approximately \(3 \times 10^8\) meters per second (m/s)
• Frequency is measured in Hertz (Hz)

To compute the wavelength, simply divide the speed of light by the frequency of the radiation. This process allows us to convert different forms of electromagnetic signals from frequency to wavelength, making it easier to compare their characteristics. This is particularly helpful in scenarios such as organizing radiation types in order of wavelength sizes as shown in the exercise.

Frequency to Wavelength Conversion

Converting frequency to wavelength is fundamental in understanding the nature of electromagnetic radiation. Whether dealing with radio waves, visible light, or any other form of electromagnetic radiation, the conversion provides valuable insights into the wave's characteristics. The equation used for this conversion,
\[ \text{Wavelength} = \frac{c}{\text{Frequency}} \] plays a pivotal role because:

• It allows us to understand how different frequencies translate into physical distances.
• Facilitates comparison between various forms of radiation across the electromagnetic spectrum.
• Enables us to determine out of a set range, what specific part of the electromagnetic spectrum the wave belongs to.

For instance, in the original exercise, the wavelengths of FM radio and mobile phone radiation were determined using their respective frequencies. This process highlights the versatile nature of electromagnetic waves and provides a unified framework for handling different wave types.

Electromagnetic Spectrum

The electromagnetic spectrum represents the entire range of electromagnetic radiation types, ordered by wavelength or frequency. It spans from low-frequency radio waves to high-frequency gamma rays. Different forms of radiation, such as visible light, UV light, microwaves, and radio waves, fall within this spectrum, each with unique wavelength characteristics.

• **Radio Waves**: Longest wavelengths, used in communication like FM radio (e.g. from the exercise, \(3.22m\)).
• **Microwaves**: Shorter than radio waves, commonly used in mobile phones.
• **Infrared and Visible Light**: Range from infrared to visible light used in everyday life, such as red and yellow light.
• **Ultraviolet (UV) Light**: Short wavelengths, used for tanning and disinfection.

Understanding the electromagnetic spectrum is crucial for appreciating how electromagnetic waves interact with matter. Different wavelengths have different energies and consequently different practical applications and effects. In our everyday life, this spectrum determines how we use waves to communicate or see the world around us. The exercise of listing radiation by wavelength helps solidify these concepts by offering real-world examples of where each type fits within the spectrum.