The correct answer is option 4: x-ray.

When the outer electrons in the inner orbits of an atom move, they can transition from a higher energy level to a lower energy level. This transition emits energy in the form of electromagnetic radiation.

X-rays are a type of electromagnetic radiation that have a high frequency and short wavelength. They are produced when electrons in an atom undergo certain transitions, such as when an electron from an outer shell jumps to a lower shell or is expelled from the atom altogether. These transitions generate x-ray photons, which are highly energetic and can penetrate materials, making them useful in medical imaging and industrial applications.

Option 1 - a-ray and option 2 - 0-ray are not correct answers because there is no such known radiation produced by the movement of outer electrons. Option 3 - y-ray is also incorrect as gamma rays are usually produced through nuclear processes and not by the movement of electrons.