Exposure to gamma rays can kill you, whereas exposure to radio waves is not harmful. Why is this so?

Gamma rays sit at the extreme end of the electromagnetic spectrum. They possess exceedingly high frequencies, typically from \(3 \times 10^{19}\text{ Hz}\to 3 \times 10^{23}\text{ Hz}\) and remarkably short wavelengths, less than 10 picometers. Due to their energetically packed waves, they are robust penetrators, having the ability to pass through almost any material.
The critical attribute that makes gamma rays exceptionally significant, and hazardous, is their ability to ionize atoms. They carry enough energy to knock electrons out of their orbit, leading to the formation of ions. This ionizing process can wreak havoc on biological tissues, potentially causing cell death, DNA mutations, and ultimately leading to illnesses like cancer. It’s no wonder that gamma radiation is often used with extreme caution in medical treatments and handled with sophisticated shielding in industrial applications.
While the destructive power of gamma rays might seem fearsome, it’s precisely their high energy that makes them invaluable for certain diagnostic procedures such as PET scans, where they help to visualize the inner workings of the human body in exceptional detail.

Radio waves represent the other end of the spectrum: where energy relaxes, and wavelengths stretch out. They range from 3 kHz to 300 GHz in frequency, boasting wavelengths that can reach up to 100 kilometers. This low end of the electromagnetic spectrum translates into a much lower energy, making radio waves benign to organic tissue.
Their long wavelengths and low energy mean that radio waves don’t have the muscle to ionize atoms; they simply do not carry enough potency to disrupt molecular structures. This feature allows them to fill the air around us without posing a danger to our health. We regularly utilize radio waves to carry information across vast distances, from the broadcasting of a morning radio program to the synchronization of GPS systems — all without affecting the living cells they quietly glide past.

Ionizing radiation is a term assigned to the more energetic portion of the electromagnetic spectrum, which includes not just gamma rays but also X-rays and part of the ultraviolet spectrum. These waves are skilled enough to ionize atoms and molecules they encounter, changing their chemical properties and setting off potentially dangerous biological reactions.
This ionization process is a double-edged sword. It’s the primary reason certain types of electromagnetic radiation are hazardous to human health, being capable of causing cancer and other genetic damage. However, this same property is employed in sterilizing medical equipment, killing bacteria and viruses, and in targeted cancer treatments. In these controlled environments, the ionizing nature of this radiation can be put to positive use, showcasing how the management and understanding of risks are crucial in harnessing the power of ionizing waves.

Every wave in the electromagnetic spectrum is characterized by its frequency and wavelength. The frequency () indicates how many wave peaks pass a particular point per second, expressed in hertz (Hz), while the wavelength () measures the distance over which the wave's shape repeats. It’s the symbiotic relationship between these two features that determines the energy of electromagnetic waves.
The spectrum itself is a continuous range, with waves at lower frequencies such as radio having longer wavelengths and thus less energy. As the frequency amps up, so does the energy, culminating in the short-wavelength, high-frequency gamma rays. It’s this differing energy that is responsible for the varying effects these waves can have when interacting with matter, highlighting how the intricacies of frequency and wavelength underpin the expansive range of electromagnetic phenomena we observe and utilize.