Use the Bohr model of the hydrogen atom to explain the emission spectrum of hydrogen.
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In short it's basically when an electron from the higher energy state drops into the lower energy state.
\[\Delta E = hf\]
The longer version explanation:
The absorption of photons occurs where their energy matches one of the permitted energy transitions - their absorption provides the energy for electrons to 'climb' the set of permitted energy levels .. either directly or in stages between a lower and higher level.
Since the set of permitted energy levels are specific and unique to a given element the range of specific absorptions/emissions are identical for all atoms of that element,so enabling different elements to be recognised and distinguished.
When the absorbed photons are removed from incident light containing the full spectrum, their absence is seen as a series of fine black lines on an otherwise continuous spectrum background.
So an emission spectra indicates the frequencies of emitted photons as electrons within the atoms return to their 'ground' states .. .. and absorption spectra record the absorption of electromagnetic radiation - as photons of specific energies, that put electrons into the higher, permitted energy levels within an atom.