Calculate the wavelength of each frequency of electromagnetic radiation, assuming four significant figures: a. 100.2 MHz (typical frequency for FM radio broadcasting) b. 1070 kHz (typical frequency for AM radio broadcasting) c. 835.6 MHz (common frequency used for cell phone communication).

Name: Chemistry: A Molecular Approach
Author: Tro
ISBN: 9780137832217

Verified step by step guidance

Identify the formula to relate frequency and wavelength: \( c = \lambda \nu \), where \( c \) is the speed of light (\( 3.00 \times 10^8 \) m/s), \( \lambda \) is the wavelength, and \( \nu \) is the frequency.

Rearrange the formula to solve for wavelength: \( \lambda = \frac{c}{\nu} \).

Convert the given frequency to hertz (Hz) if necessary: a. 100.2 MHz = 100.2 \(\times\) 10^6 Hz, b. 1070 kHz = 1070 \(\times\) 10^3 Hz, c. 835.6 MHz = 835.6 \(\times\) 10^6 Hz.

Substitute the speed of light and the converted frequency into the formula for each case to find the wavelength: \( \lambda = \frac{3.00 \times 10^8}{\nu} \).

Calculate the wavelength for each frequency, ensuring the answer is expressed with four significant figures.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Electromagnetic Spectrum

The electromagnetic spectrum encompasses all types of electromagnetic radiation, which vary in frequency and wavelength. It includes radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays. Understanding the spectrum is crucial for identifying the properties and applications of different types of radiation, such as FM and AM radio frequencies.

Wave-Particle Duality

Wave-particle duality is a fundamental concept in quantum mechanics that describes how electromagnetic radiation exhibits both wave-like and particle-like properties. This duality is essential for understanding phenomena such as interference and diffraction, which are relevant when discussing the behavior of radio waves and their interactions with various media.

Wavelength and Frequency Relationship

The relationship between wavelength and frequency is described by the equation c = λν, where c is the speed of light, λ is the wavelength, and ν is the frequency. This inverse relationship means that as frequency increases, wavelength decreases, and vice versa. This concept is vital for calculating the wavelength of electromagnetic radiation based on given frequencies.