The Sun emits a broad spectrum of electromagnetic (EM) waves because it undergoes a process called black-body radiation. A black body is an idealized object that absorbs all incident radiation and emits radiation across a wide range of wavelengths.
The Sun's core is a site of nuclear fusion where hydrogen atoms combine to form helium, releasing an enormous amount of energy in the process. This energy moves toward the surface of the Sun through a series of energy transfers, and as it does so, it gets converted into thermal energy. This thermal energy is then radiated outwards in the form of electromagnetic waves.
According to Planck's law of black-body radiation, the intensity and distribution of radiation emitted by an object depend on its temperature. The Sun's temperature is around 5,500 degrees Celsius (9,932 degrees Fahrenheit) at its surface, and this high temperature causes it to emit a wide range of electromagnetic waves.
The distribution of emitted radiation follows what is known as the Planck spectrum, which encompasses a continuous range of wavelengths and frequencies. As the temperature of the Sun decreases with increasing distance from the core, the intensity of the radiation decreases at shorter wavelengths and shifts toward longer wavelengths.
This broad spectrum of radiation emitted by the Sun includes radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and even gamma rays. Each of these types of electromagnetic waves corresponds to a different range of wavelengths and has its own properties and interactions with matter.
So, the Sun emits a broad spectrum of electromagnetic waves because of its high temperature, which leads to black-body radiation, resulting in the emission of radiation across a wide range of wavelengths.