The Electromagnetic Spectrum

The Wave Equation: The relationship between speed ($v$), frequency ($f$), and wavelength ($\lambda$) is defined by $v = f\lambda$. For EM waves in a vacuum, this becomes $c = f\lambda$.

Inverse Proportionality: Because the speed $c$ is constant, frequency and wavelength are inversely proportional; as frequency increases, wavelength must decrease to maintain the same product.

Energy-Frequency Relationship: The energy carried by an EM wave is directly proportional to its frequency. High-frequency waves (like Gamma rays) carry significantly more energy per photon than low-frequency waves (like Radio waves).

Propagation: Unlike mechanical waves (sound or water), EM waves do not require a medium (matter) to travel because they are self-sustaining oscillations of fields.

Radio Waves: Have the longest wavelengths and lowest frequencies; primarily used for long-range communication and broadcasting.

Microwaves: Used for satellite communications and radar because they can penetrate the atmosphere, as well as for cooking by exciting water molecules.

Infrared (IR): Emitted by all warm objects; used in thermal imaging, remote controls, and fiber optic communication.

Visible Light: The only part of the spectrum detectable by the human eye, ranging from red (longest $\lambda$) to violet (shortest $\lambda$).

Ultraviolet (UV): Carries enough energy to cause chemical reactions; used in fluorescent lamps and sterilization, but can cause skin damage.

X-rays: High-energy waves capable of penetrating soft tissue but being absorbed by dense materials like bone, making them ideal for medical imaging.

Gamma Rays: The highest frequency and energy; produced by nuclear transitions and used in medical sterilization and cancer treatment.

Memorize the Order: Use a mnemonic to remember the order from longest to shortest wavelength: Raging Martians Invaded Venus Using X-ray Guns (Radio, Micro, IR, Visible, UV, X-ray, Gamma).

Check the Units: Wavelengths are often given in nanometers ($1 nm = 1 \times 10^{-9} m$) or micrometers. Always convert to meters before using the wave equation.

Constant Speed Assumption: Unless the question specifies a different medium (like glass or water), always assume the speed is $3 \times 10^8 m/s$.

Reasonableness Check: If you calculate a frequency for a Gamma ray and it is lower than that of a Radio wave, you have likely inverted the relationship in your calculation.