Again: what kind of radiation? Electromagnetic radiation from the visible spectrum up to x-rays is being emitted by the electrons "surrounding" the nucleus.
Typicaly electrons get kicked to higher energy levels (get excited) and emit the excess energy when "falling" back to their original level.
Infrared radiation is usually the result of oscillations of atoms in molecules, around interatom (chemical) bonds.
Alpha radiation occurs when a certain instable nucleus breaks up and emits an Alpha particle, consisting of two neutrons and two protons each (a helium nucleus, positively charged). The resulting nucleus will be more stable, but will be excited as well, usually loosing the excess energy via a gamma photon.
Beta minus radiation occurs if a neutron breaks up into an electron, a proton and a neutrino. The proton will form part of the resulting new nucleus (an element one position further up the periodic table), while the electron will be emitted from the nucleus with high energy, as will be the neutrino. Since neutrinos rarely interact with matter, in most cases it will not be detected. Again, excess energy will be emitted via a Gamma quantum.
Another source of gamma radiation is to excite a nucleus e.g. through absorbtion of gamma radiation of resonant frequency and then letting it be emitted, similar to flourescence. This is used in Mössbauer spectroscopy (the resonace frequency of a nucleus is dependend on the chemical bond of the atom and will vary slightly).
Neutron radiation usualy gets emitted by breaking up nuclei, e.g. in a nuclear fission reactor U235 gets bombarded with slow (thermic) neutrons, the impact of a neutron on a U235 nucleus will cause the new compound nucleus ( U236, very instable) to oscillate and break up into Y96, I139 and 3 neutrons. These, being instable themselves, will again break up, emitting mostly beta radiation until they reach the stable nuclei of Ba138 and Mo 95. Another source would be to bombard Be 9 with Alpha particles, causing it to emit neutrons ( a neutron source we used during our basic experimental physics lab class in university to irradiate other elements, e.g. silver, with the neutrons to cause them to change. We then measured the resulting halflifes and gamma spectra of the resulting new elements).
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