Why do hot things radiate? Its a broad question, so I'll tell you the situation where I stumbled across this.
In corona discharge, or when any electron beam travel through air, it hits the air molecules (consitituent molecules in mixture) and they get excited and lose energy afterwards in form of photons.

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*how kinetic energy of electron transfers into potential energy of electron-nucleus potential energy? Why can't the nucleus simply get faster (momentum transfer)?

*why the kinetic energy simply results into increase in temperature and no photo-emmision? Even you can feel the heat in neighborhood of discharge, but still it's not a good explanation, that cause the air is a bad conductor, it gives out energy in photoemmision.

*If this is assumed that somehow electron gets excited, why does this spontaneous emmision happens?

These are some questions I can thought of containing a whole range of phenomenons. But they all come under same umbrella question.
 A: 
how kinetic energy of electron transfers into potential energy of electron-nucleus potential energy? Why can't the nucleus simply get faster (momentum transfer)?

The electron undergoes a scattering interaction with some component of the atom. Essentially, the electron undergoes electrical repulsion (or equivalently, photon exchange, if you like), which transfers momentum to some part of the atom. At energies significantly lower than the ionization energy, the scattering tends to be elastic, where the electron interacts with the whole atom at once, both with the electron cloud and the nucleus; during elastic scattering, the atom recoils as a whole. At energies approaching or exceeding the ionization energy, the scattering tends to be inelastic, where the electron interacts with some individual part of the atom, to either excite it to a higher energy state or separate it from the atom entirely.
In inelastic scattering, the object that the incoming electron interacts with is almost always another electron, rather than the nucleus, for two main reasons:

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*The electron cloud is much larger than the nucleus, so there's a much bigger "target", and


*The electron cloud is in the way of the nucleus, so an electron interacting exclusively with the nucleus would have to pass through the electron cloud without interacting somehow, which is unlikely.

why the kinetic energy simply results into increase in temperature and no photo-emmision?

An increase in temperature implies an increase in photo-emission. The blackbody radiation emitted by an object increases when the temperature increases.

Even you can feel the heat in neighborhood of discharge, but still it's not a good explanation, that cause the air is a bad conductor, it gives out energy in photoemmision.

Good conductors have a supply of relatively free-moving electrons that can be pushed around with only a little energy. Bad conductors do not; their electrons are tightly bound to their atoms, and in order to move the electrons around independently of the nuclei, you must first rip the electrons off of the atoms. This takes a lot of energy. The thing to keep in mind is that generally, processes in nature are symmetric, in a sense: if it requires a large amount of energy to do a particular thing, then doing that thing in reverse will release a large amount of energy. So, since it takes a lot of energy to separate an electron and a nucleus in an insulator, putting an electron and an ionized atom back together will release a lot of energy. That's where the "photoemission" that you're talking about comes from: it's light released when free electrons recombine with ions to form neutral atoms again.

If this is assumed that somehow electron gets excited, why does this spontaneous emmision happens?

You should probably draw a distinction between "excited" and "ionized". An excited electron is still bound to an atom, but in a higher energy level, while an ionized electron is completely free from an atom. What's happening in corona discharge is related to ionization, not excitation. And the light that you see comes from the fact that a free electron and an ion electrically attract each other, and therefore release a great deal of energy in the form of light when they come together.
