Final answer:
If an electromagnetic wave has a high frequency, it has high energy and a small wavelength, like gamma rays. Gamma rays are part of the electromagnetic spectrum, with much shorter wavelengths than radio waves and are used in medical applications due to their high energy.
Step-by-step explanation:
If an electromagnetic wave has a high frequency, it also has high energy and small wavelength. The correct answer to the student's question is a. high energy and small wavelength such as gamma rays. Gamma rays have very short wavelengths (on the order of 10-12 meters) and high frequencies, which contribute to their high energy levels.
Within the electromagnetic spectrum, energy is directly proportional to frequency, meaning higher frequency waves have more energy. This concept is tied to the idea that electromagnetic radiation can be thought of both as waves and as a stream of particles called photons. The energy carried by a photon depends on its frequency. For example, gamma rays are at the high-frequency end of the spectrum and have enough energy to be used in medical applications to kill cancer cells and sterilize medical equipment.
In contrast, radio waves, which are at the low-frequency end of the spectrum, have longer wavelengths and carry less energy. Radio waves are commonly used for communication due to their ability to travel long distances with less energy. Therefore, options b, c, d, and e do not accurately represent the relationship between frequency, wavelength, and energy in the context of electromagnetic waves.