Thermionic emission : When a metal is heated to a high temperature, the free electron gain kinetic energy and escape from the surface of the metal.

Secondary emission : When an electron strikes the surface of a metallic plate, it emits other electrons lion the surface.

Photoelectric emission : Emission of electrons lion tire metal surface on irradiation with radiation of suitable frequency.

X-rays emission : They are due to transitions in the inner energy levels of the atom.

Explanation:

The emission of electrons refers to the process of electrons being released or emitted from a material. It can occur through various mechanisms such as thermionic emission, photoelectric emission, and secondary emission. However, X-ray emission does not involve the emission of electrons.

Thermionic Emission:
Thermionic emission is the process by which electrons are emitted from a heated material. When a material is heated to a sufficiently high temperature, the thermal energy causes electrons to overcome the energy barrier at the surface and escape into the surrounding space. This process is commonly used in thermionic valves or vacuum tubes.

Photoelectric Emission:
Photoelectric emission occurs when photons (particles of light) strike a material surface and transfer their energy to electrons, causing them to be emitted. This phenomenon was first explained by Albert Einstein and is the basis for the photoelectric effect. The energy of the photons must exceed the work function (minimum energy required to remove an electron) of the material for photoelectric emission to occur.

Secondary Emission:
Secondary emission is a process in which electrons are emitted from a material surface due to the impact of high-energy electrons or ions. When these energetic particles strike the surface, they can knock out additional electrons from the material, causing secondary emission. This effect is utilized in devices such as photomultiplier tubes and electron multipliers.

X-ray Emission:
X-ray emission, on the other hand, does not involve the emission of electrons. X-rays are a type of electromagnetic radiation that is generated through processes such as atomic transitions or the interaction of high-energy particles with matter. They are typically produced by accelerating electrons and directing them at a target material, causing the atoms in the target to emit X-rays. However, the X-rays themselves do not involve the emission of electrons.

Therefore, among the given options, X-ray emission is the process in which the emission of electrons does not take place.