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Line spectra, also known as atomic emission spectra or simply emission spectra, are the characteristic patterns of bright colored lines that are emitted by elements when they are excited by energy sources such as heat or electricity. When a hydrogen atom is energetically excited, an electron transitions from a lower energy level to a higher one. When the electron falls back to its original energy level, a photon (packet of electromagnetic radiation) is emitted, and the energy of the photon corresponds to the difference in energy levels. The emitted photons correspond to specific frequencies and wavelengths, producing the pattern of discrete colored lines that make up the line spectra.

Niels Bohr's theory of quantized energies states that an electron within an atom can only exist at certain fixed energy levels. These energy levels are quantized, meaning that the electron can only occupy specific, discrete energy states. In the case of the hydrogen atom, each energy level is assigned a specific integer quantum number, "n", the principal quantum number. Bohr's theory also states that energy is only emitted or absorbed when the electron makes a transition between energy levels. When an electron moves from a higher energy level to a lower one, energy in the form of a photon is emitted, and vice versa when the electron transitions to a higher energy level.

The existence of line spectra is consistent with Bohr's theory of quantized energies for the electron in the hydrogen atom because the observed line spectra are a direct result of the electron transitions between discrete energy levels. According to Bohr's theory, energy is emitted in the form of photons when an electron jumps from higher energy levels to lower ones, and the energy associated with each photon corresponds to the difference in energy between the initial and final energy levels. This explains the presence of discrete colored lines, as each line corresponds to the emitted photon with a specific energy, frequency, and wavelength. To summarize, line spectra are consistent with Bohr's theory of quantized energies for the electron in the hydrogen atom because they represent the discrete energy releases that correspond to electron transitions between specific quantized energy levels. This connection between theory and observed phenomena provides empirical support for Bohr's theory and its ability to describe atomic behavior.