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When we heat a collection of atoms, we supply energy to the electrons of the atoms. When the energy equals the minimum energy required for the first transition of the electron the electron absorbs energy and jumps to the next allowed energy state. However, the next subsequent transition requires even less energy and as energy supplied depends on the temperature difference which more or less remains the same, the energy available to the electron now is way more than it requires and so what will happen now?

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There are a number of misconceptions here. To start with heat is a thermodynamic concept, and thermodynamics is emergent from the underlying statistical level.

When we heat a collection of atoms, we supply energy to the electrons of the atoms.

We provide kinetic or rotational energy to the whole atoms and molecules, not the electrons. Temperature is connected to the average kinetic energy.

When the energy equals the minimum energy required for the first transition of the electron the electron absorbs energy and jumps to the next allowed energy state.

Atomic transitions need keV energies which means very high temperatures for the single atoms/molecules so that collisions can excite energy levels.

However, the next subsequent transition requires even less energy and as energy supplied depends on the temperature difference which more or less remains the same, the energy available to the electron now is way more than it requires and so what will happen now?

For very high temperatures the atoms ionize and we go into the plasma phase, which in nature is mostly found in very hot flames and is necessary for star models and studies .

phase diagram

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