An ion is an atomic particle that is electrically charged, either negatively or positively by loss or addition of one or more electrons. The simplest ions are for example hydrogen ions (a proton, H+), or an alpha particle (helium ion, He2+).
Positively-charged ions have fewer electrons than protons. They are cations due to the attraction to cathodes.
Negatively charged ions have more electrons in the electron shells than they have protons in the core. Due to their attraction to anodes they are named anions.

Characterization of atoms by their nuclear properties, as the number of protons and the number of neutrons. The different nuclides of an element are its isotopes (equal proton number, but different neutron numbers). Isomers of this particular nuclide are equal in the proton and mass numbers, but differ in their energy content. Unstable nuclides which are radioactive are called radionuclides.

See also Isotope, Isomer and Decay.

[Beta Plus Decay] If an atom is unstable because there are too many protons in the nucleus, a proton is converted into a neutron and a positron is emitted. The atomic mass of the atom stays unchanged, but the number of protons increases by one, the number of neutrons decreases by one, which transforms the atom to a different element.

See also Beta Decay.

Alpha particles consist of two neutrons and two protons (nucleus of He), have a positive charge of 2 and a velocity in air of approximately one-twentieth the speed of light.
Discovered by Ernest Rutherford in 1899 (Rutherford-Bohr planetary atom model) alpha particles became emitted by very large atoms in an unstable energy state (high atomic number mostly over 82, with a too low neutrons//protons ratio (e.g. <= 1.5)).
Through their relative slow travel speed, they get stopped by e.g. a thin sheet of paper or the outer layers of human skin or travel only inches; once stopped they pick up free electrons and become helium.
These alpha particles are only dangerous to humans when the alpha-emitting material is inhaled or ingested (it causes damage that may lead to cancer) or comes into contact with the lens of the eye, caused by their less penetrating properties.

There are two kinds of beta decay: beta minus and beta plus decay. The differentiation depends on the charge of the emitted particle.
At the beta plus decay in the nucleus a proton changes to a neutron and emits a positron and a neutrino. The atom is after the decay a different element, but with the same number of particles in the nucleus.
At the beta minus decay in the nucleus a neutron changes to a proton and emits an electron and an antineutrino. As with the beta plus decay the atom changes to a different element but with the same number of particles in the nucleus.
Sometimes the electron capture is mentioned as a third kind of beta decay.
Beta decay is used for example in positron-electron tomography or in iodine-131 therapy.

See also Electron Capture.