Electromagnetic spectrum

All electromagnetic waves, regardless of source, obey one fixed relationship between their wave speed, frequency $\nu$ and wavelength $\lambda$:

where: $c \approx 3\times10^8\ \text{m/s}$ is the speed of light in vacuum (a universal constant, the same for every region of the spectrum), $\nu$ is the frequency in hertz, and $\lambda$ is the wavelength in metres. Because $c$ is fixed, wavelength and frequency move in lockstep but in opposite directions — a wave with a short wavelength must have a high frequency, and vice versa. Photon energy rises with frequency, which is why the spectrum is conventionally listed from longest wavelength (lowest frequency, lowest energy) to shortest wavelength (highest frequency, highest energy):

• Radio waves ($\lambda$ up to several km, down to about $0.1\ \text{m}$): produced by oscillating charges in antennas driven by LC circuits; detected by tuned receiving antennas; used for broadcasting and mobile communication.
• Microwaves ($\lambda \sim 1\ \text{mm}$ to $0.3\ \text{m}$): produced by klystrons and magnetrons; detected by point-contact diodes; used in radar, satellite links, and microwave ovens.
• Infrared ($\lambda \sim 700\ \text{nm}$ to $1\ \text{mm}$): produced by hot bodies and molecular vibrations; detected by thermopiles and bolometers; used in remote sensing, night vision, and remote controls — felt directly as heat.
• Visible light ($\lambda \approx 400$–$700\ \text{nm}$): produced by electronic transitions in atoms; detected by the eye and by CCD sensors; the only region humans see, and the basis of photosynthesis.
• Ultraviolet ($\lambda \approx 1$–$400\ \text{nm}$): produced by discharge lamps and the Sun; detected by photocells; used for sterilisation and fluorescent lighting — mostly absorbed by the ozone layer.
• X-rays ($\lambda \approx 10^{-3}$–$1\ \text{nm}$): produced by fast electrons suddenly decelerated at a metal target; detected by photographic film and ionisation chambers; used in medical imaging and crystal structure studies.
• Gamma rays ($\lambda$ below about $10^{-3}\ \text{nm}$): produced by nuclear reactions and radioactive decay; detected by Geiger counters; the most penetrating, highest-energy region, used in cancer treatment and nuclear studies.

Because $c = \nu\lambda$ holds continuously across the whole range, no sharp boundary separates one region from the next — the labels are a convenience based on typical production, detection, and interaction with matter, not a fundamental physical divide. This is also why the classification is sometimes drawn with slightly different cutoff numbers in different textbooks: the physics is one continuous curve, and the fences are administrative.

An X-ray photon has a wavelength of $0.10\ \text{nm}$. A gamma-ray photon emitted by the same radioactive sample has a wavelength ten thousand times smaller, $1.0\times10^{-5}\ \text{nm}$. Find the frequency of each and compare their photon energies.

Step 1. Convert both wavelengths to metres: the X-ray wavelength is $\lambda_1 = 0.10\ \text{nm} = 1.0\times10^{-10}\ \text{m}$, and the gamma-ray wavelength is $\lambda_2 = 1.0\times10^{-5}\ \text{nm} = 1.0\times10^{-14}\ \text{m}$.

Step 2. Apply $\nu = c/\lambda$ to the X-ray photon:

This frequency sits comfortably in the X-ray range, as expected from the given wavelength.

Step 3. Apply the same relation to the gamma-ray photon:

Step 4. Compare the two. The gamma-ray frequency $\nu_2$ is exactly ten thousand times $\nu_1$, matching the given ratio of wavelengths (since $\nu \propto 1/\lambda$, a wavelength ten thousand times smaller gives a frequency ten thousand times larger). Since photon energy increases with frequency, the gamma-ray photon carries about ten thousand times more energy than the X-ray photon — consistent with gamma rays, produced by nuclear processes, being the most energetic and most penetrating part of the spectrum, well beyond X-rays produced by atomic-scale electron deceleration.

Competitive stretch

A microwave oven's magnetron is quoted as operating at $2.45\ \text{GHz}$. Using $\lambda = c/\nu = (3\times10^8)/(2.45\times10^9) = 0.122\ \text{m} = 12.2\ \text{cm}$, the wavelength falls inside the microwave band ($1\ \text{mm}$ to $0.3\ \text{m}$), confirming the label on the appliance without needing to look at a spec sheet — a two-line check any given frequency can be put through.

• Treating the different regions as fundamentally different kinds of waves — they are all electromagnetic waves obeying the same $c=\nu\lambda$; only wavelength, frequency, and hence energy differ.
• Reversing the trend across the spectrum: wavelength decreases and frequency increases as you move from radio waves to gamma rays, not the other way round.
• Assuming sharp, exact boundaries exist between adjacent regions — the quoted ranges are approximate, the regions overlap, and the split is by production/detection convention, not a physical wall.
• Confusing production mechanisms — X-rays come from fast electrons suddenly decelerated at a metal target (an X-ray tube), while gamma rays come from radioactive nuclei; swapping the two is a common slip.

Ask the tutor: Want a quick drill identifying which spectrum region a given wavelength or frequency falls in, or a recap of production/detection methods for each region?