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The dark lines observed in an atom's absorption spectrum are directly related to the bright lines observed in its emission spectrum. To understand this relationship, it is necessary to first understand how both spectra are produced.

When an atom is subjected to a continuous spectrum of light, such as white light, it can absorb specific wavelengths of light that correspond to the energy differences between its quantized energy levels. These energy transitions occur when electrons in the atom's outer shells are excited to higher energy levels by absorbing photons of specific energies. The absorbed photons are essentially "missing" from the continuous spectrum, resulting in dark absorption lines at those specific wavelengths in the absorption spectrum.

On the other hand, when the same excited electrons in an atom return to lower energy levels, they release energy in the form of photons. These emitted photons have discrete energies corresponding to the energy differences between the energy levels involved in the transition. The emitted photons form the bright lines observed in the emission spectrum of the atom.

The relationship between the absorption and emission spectra is explained by the concept of quantized energy levels in atoms. Each atom has a unique set of energy levels, and the transitions between these levels are associated with specific energies. The absorption spectrum reveals the energies required to excite electrons from lower to higher energy levels, while the emission spectrum displays the energies released when electrons return to lower energy levels.

Because the energy levels of atoms are quantized, the absorption and emission processes occur at distinct, discrete energies, resulting in the appearance of sharp lines in the spectra. The specific energies associated with these lines depend on the atom's electronic structure and the energy level differences within it.

In summary, the dark lines in an atom's absorption spectrum represent the energies absorbed by the atom when its electrons are excited to higher energy levels. Conversely, the bright lines in the atom's emission spectrum represent the energies released when the excited electrons return to lower energy levels. The correspondence between the dark absorption lines and the bright emission lines arises from the quantized energy levels of the atom and the specific energy differences associated with its electronic transitions.

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