Electromagnetic Radiation: Frequency, Wavelength, and Interference

Electromagnetic Radiation

Key Constants and Definitions

Electromagnetic radiation is a form of energy that travels through space as waves. Two important properties of these waves are wavelength (λ) and frequency (ν). The speed of light (c) is a fundamental constant in these calculations.

• Speed of light (c): $c = 2.99792458 \times 10^8$ m/s

• Avogadro's number (NA): $N_A = 6.022 \times 10^{23}$ mol-1

• Wavelength (λ): The distance between successive crests of a wave, measured in meters (m) or nanometers (nm).

• Frequency (ν): The number of wave cycles that pass a given point per second, measured in hertz (Hz).

• Relationship between frequency and wavelength:

$\nu = \frac{c}{\lambda}$

Where $\nu$ is frequency, $c$ is the speed of light, and $\lambda$ is wavelength.

Practice Problems

1. Calculating Frequency from Wavelength

Given: A red light has a wavelength (λ) of 625 nm. Find its frequency (ν).

• Step 1: Convert wavelength to meters: $625 \text{ nm} = 625 \times 10^{-9} \text{ m}$

• Step 2: Use the formula $\nu = \frac{c}{\lambda}$

• Step 3: Substitute values: $\nu = \frac{2.99792458 \times 10^8 \text{ m/s}}{625 \times 10^{-9} \text{ m}}$

• Step 4: Calculate the result to find frequency in Hz (s-1).

Example: This calculation is commonly used to determine the color of light in spectroscopy.

2. Calculating Wavelength from Frequency

Given: The frequency of light emitted by a barcode scanner is 462 THz ($1 \text{ THz} = 10^{12} \text{ Hz}$). Find the wavelength in nanometers.

• Step 1: Convert frequency to Hz: $462 \text{ THz} = 462 \times 10^{12} \text{ Hz}$

• Step 2: Use the formula $\lambda = \frac{c}{\nu}$

• Step 3: Substitute values: $\lambda = \frac{2.99792458 \times 10^8 \text{ m/s}}{462 \times 10^{12} \text{ Hz}}$

• Step 4: Convert the result from meters to nanometers ($1 \text{ m} = 10^9 \text{ nm}$).

Example: This calculation is useful in identifying the type of electromagnetic radiation used in devices.

3. Interference Patterns: Constructive and Destructive

When two waves overlap, they can interfere in two main ways:

• Constructive Interference: Occurs when the crests of two waves align, resulting in a wave of greater amplitude.

• Destructive Interference: Occurs when the crest of one wave aligns with the trough of another, resulting in reduced or zero amplitude.

Example: Interference patterns are observed in experiments such as the double-slit experiment, demonstrating the wave nature of light.

4. Electromagnetic Radiation Table

The electromagnetic spectrum includes various types of radiation, each with characteristic frequency, wavelength, and energy. The table below compares different types of radiation:

Type of Radiation	Order of Frequency	Order of Wavelength	Order of Energy
Microwaves	Low	Long	Low
Green Light	Medium	Medium	Medium
Gamma Rays	High	Short	High

Additional info: The electromagnetic spectrum ranges from radio waves (lowest frequency, longest wavelength) to gamma rays (highest frequency, shortest wavelength). Visible light is in the middle of the spectrum.