Yes, in a vacuum, all wavelengths of light travel at the same speed, which is approximately 299,792 kilometers per second (often rounded to 300,000 kilometers per second for simplicity), denoted by the symbol "c." This constant speed of light in a vacuum is a fundamental physical constant and is one of the fundamental postulates of Albert Einstein's theory of relativity.
It's important to note that the speed of light can vary when light passes through different materials, such as air, water, or glass. In such cases, the speed of light is slower than the speed in a vacuum, and it depends on the refractive index of the material. However, within a given medium, the different wavelengths of light still travel at the same speed. This property leads to phenomena such as refraction and dispersion, where different wavelengths are bent or separated due to their varying speeds in a material.