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A textbook mentions:

A bulb has a solid filament that is heated. Energy levels in solids overlap, so all energy changes for the electrons are allowed. This means the electrons can emit photons with any energy, producing a continious spectrum when a solid is heated.

I don't understand what it means by 'overlap of energy levels', and how this could lead to a continious spectrum. Not all solids produce a continuous spectrum, so what does this phrase mean?

Source: "AQA A Level Physics (Year 1 and Year 2)", chapter "Line spectra and continuous spectra"

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the electrons in a hot object are not jumping between discrete energy levels. the atoms themselves are vibrating from the thermal agitation and in doing so their energy levels exist in a continuum, and give rise to a smooth distribution of frequencies.

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  • $\begingroup$ so atoms themselves have discrete vibration levels? $\endgroup$
    – XXb8
    Commented May 17, 2020 at 17:37
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    $\begingroup$ the contiuous is in contrast with the dicrete energy spectra from transitions within an atom. hyperphysics.phy-astr.gsu.edu/hbase/quantum/atspect2.html . The vibrational levels of atoms in a lattice in room temperatures are not in the optical range, part of the black body radiation in the infrared. When heated the BB radiation goes towards visible. $\endgroup$
    – anna v
    Commented May 17, 2020 at 18:18
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All matter in bulk emits electromagnetic radiation modeled as black body radiation. This radiation was known but could not be fitted with classical electromagnetic theory. Black body radiation is fitted with quantum mechanics and it is one of the reasons quantum mechanics was necessarily developed.

The spectrum of this radiation is temperature dependent, the higher the temperature the larger the frequencies. A cold solid will not radiate in visible frequencies. A heated solid as the wire in a light bulb radiates a lot in the visible.

This statement:

Energy levels in solids overlap, so all energy changes for the electrons are allowed. This means the electrons can emit photons with any energy, producing a continious spectrum when a solid is heated'

This paragraph tries to explain why there is a continuous and not a discreet spectrum in the light from a light bulb. Black body radiation is a better mathematical description , as you will see if you read the link.

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