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The distinctive red-orange glow in the emission spectrum of neon arises from electron transitions between specific energy states. When neon atoms are excited by an electrical discharge, electrons jump to higher energy levels, in this case, the $3p$ states. As the electrons return to slightly lower, but still excited, $3s$ states, they emit light, producing the characteristic red-orange color.
In gases like neon, the absorption spectrum consists only of wavelengths corresponding to transitions that start from the ground state. This is because, at room temperature, nearly all neon atoms remain in the ground state, with very few reaching excited states spontaneously. Consequently, there is an insignificant number of neon atoms in the $3s$ state to absorb the emitted red-orange light.
In a glass tube filled with neon at room temperature, absorption of light is limited to wavelengths that ground-state neon atoms can absorb. However, these absorption lines occur at very short wavelengths (below 100 nm), far outside the range of visible light (400-700 nm). The lowest energy levels that neon atoms can transition to from the ground state are more than 16 electron volts (eV) above the ground state, necessitating much higher energy (shorter wavelength) photons than those found in visible light.
As a result, at room temperature, neon remains transparent to all wavelengths within the visible light spectrum because none of its absorption lines fall within this range. This transparency explains why neon's characteristic glow can be seen without interference.
