Problem 4 - Chemistry and Global Awareness

Question

You are exposed to radiation that has a wavelength of \(50 \mu \mathrm{m}\). What is the frequency of this radiation? Where does this radiation appear? Is this radiation ionizing or nonionizing?

Step-by-Step Solution

Answer

Frequency: 6 THz, appears in far-infrared, and is nonionizing radiation.

Step 1: Understand the relationship between wavelength and frequency

The frequency (\(f\)) and wavelength (\(\lambda\)) of electromagnetic waves are related by the speed of light (\(c\)): \[c = f\cdot \lambda\]where \(c\) is approximately \(3 \times 10^8\) meters per second. We're given \(\lambda = 50 \mu \mathrm{m} = 50 \times 10^{-6}\) meters. The goal is to find \(f\).

Step 2: Rearrange the formula to solve for frequency

Rearrange the equation \(c = f\cdot \lambda\) to solve for frequency \(f\):\[f = \frac{c}{\lambda}\]

Step 3: Substitute known values into the formula

Substitute the given values into the rearranged formula: \[f = \frac{3 \times 10^8}{50 \times 10^{-6}}\] This will give us the frequency in hertz.

Step 4: Calculate the frequency

Carry out the calculation:\[f = \frac{3 \times 10^8}{50 \times 10^{-6}} = 6 \times 10^{12} \text{ Hz}\] Thus, the frequency is \(6 \times 10^{12} \text{ Hz}\) (or \(6\) terahertz).

Step 5: Determine the region of the electromagnetic spectrum

Radiation with a wavelength of \(50 \mu \mathrm{m}\) falls in the far-infrared region of the electromagnetic spectrum, which ranges from \(15 \mu \mathrm{m}\) to \(1 \text{ mm}\).

Step 6: Classify the radiation as ionizing or nonionizing

Radiation is classified as ionizing if it has enough energy to remove tightly bound electrons from atoms. Infrared is nonionizing because its energy is lower than the threshold needed to ionize atoms. Nonionizing radiation does not have enough energy to cause ionization in biological tissues.

Key Concepts

Wavelength and Frequency Relationship

Understanding the relationship between wavelength and frequency is crucial for grasping the concepts of the electromagnetic spectrum. Simply put, the frequency of a wave (\(f\)) is inversely related to its wavelength (\(\lambda\)). This relationship is defined by the equation: \[ c = f\cdot \lambda \]Here,

• \(c\) is the speed of light, approximately 3 \times 10^8 meters per second.
• \(f\) is the frequency in hertz (Hz).
• \(\lambda\) is the wavelength in meters.

To find the frequency when the wavelength is given, you rearrange the formula to: \[ f = \frac{c}{\lambda} \] This equation lets us calculate the frequency (which tells us how many wave cycles pass a point per second) when we know the wavelength. For the example of a wavelength of 50 μm, we'd use 50 \times 10^{-6} metersto calculate the frequency.

Infrared Radiation

Infrared radiation is part of the electromagnetic spectrum with wavelengths longer than visible light but shorter than microwaves. When you think of infrared, imagine heat. The warmth you feel from the sun or a campfire is due to infrared radiation. Infrared radiation is divided into three main categories:

• Near-infrared - Wavelengths between 0.75 to 1.4 µm
• Mid-infrared - Wavelengths between 1.4 to 3 µm
• Far-infrared - Wavelengths from 15 µm up to 1 mm

In the context of the exercise, the wavelength of 50 μm falls into the far-infrared category. This means the radiation is less energetic than mid and near-infrared but is still important in fields like astronomy and remote sensing. Far-infrared radiation is often used in thermal imaging cameras and in some medical therapies to provide heat treatment.

Nonionizing Radiation

Nonionizing radiation refers to types of electromagnetic radiation that do not carry enough energy to ionize atoms or molecules. Ionization occurs when radiation strips away electrons from an atom, potentially causing chemical reactions. Nonionizing radiation includes:

• Microwaves
• Infrared Radiation
• Visible Light
• Radio Waves
• Ultraviolet Light (only under specific conditions)

Infrared radiation is classified as nonionizing. While nonionizing radiation, like infrared, doesn't have the energy to remove tightly bound electrons, it can still pose different effects. For instance, prolonged exposure to infrared radiation might cause thermal injury, although such occurrences are rare. The main use of nonionizing radiation, particularly infrared, is in everyday applications like heating, communications, and certain types of medical treatments that focus on heating tissues.