While the Sun primarily emits visible light and infrared radiation, it also produces a small amount of gamma rays, which are generated during nuclear fusion reactions within its core. These gamma rays are extremely energetic and have wavelengths shorter than 0.01 nanometers.

However, it's important to note that:

* Gamma rays from the Sun are absorbed by the Sun's atmosphere: They don't reach the Earth's surface.

* The Sun also emits X-rays: These have slightly longer wavelengths than gamma rays but are still very energetic and can be harmful to living organisms.

* The Sun's most intense radiation is in the visible light spectrum: This is why we can see it.

So, while gamma rays are the shortest wavelength radiation emitted by the Sun, they don't play a significant role in our daily lives due to their absorption in the Sun's atmosphere.