Question

Why any particle when heated produce a wide range of wavelengths?

Answer 1

wavelength ranges from zero to infinity. What we tend to think of as “heat” is usually in the infrared range, starting at 700nanometers or so and getting as long as a few centimeters (microwave ovens) if you want to push it.

The thermal wavelengths of an incandescent lightbulb, for instance, cover the entire visible range in addition to infrared and some ultraviolet