If the electron in a hydrogen atom obeyed classical mechanics instead of quantum mechanics, would it emit a continuous spectrum or a line spectrum?
In classical mechanics, the electron would decelerate and emit a continous spectrum as it heads for and crashes into the nucleus.
If the electron in a hydrogen atom obeyed classical mechanics instead of quantum mechanics, it would emit a continuous spectrum of light rather than a line spectrum.
To understand why, let's consider the behavior of an electron in a hydrogen atom. According to classical mechanics, an electron moving in a circular orbit around the nucleus would continuously emit energy in the form of electromagnetic radiation. As the electron loses energy, it would spiral inward towards the nucleus.
In this scenario, the emitted radiation would be continuously changing in frequency. This is because the electron's energy would be continuously decreasing as it gets closer to the nucleus, resulting in a gradual decrease in the emitted frequency.
Ultimately, the electron would hit the nucleus, since classical mechanics predicts that it cannot stably orbit a nucleus. This would lead to the complete cessation of radiation emission.
In contrast, in quantum mechanics, the hydrogen atom's electron can only exist in certain discrete energy levels, or orbitals, around the nucleus. When the electron transitions between these energy levels, it emits or absorbs photons of specific energies, corresponding to specific wavelengths or frequencies.
Each energy level transition produces a specific spectral line in the atom's emission or absorption spectrum, resulting in a line spectrum rather than a continuous spectrum.
So, if the electron obeyed classical mechanics, it would emit a continuous spectrum of light, whereas in reality, due to quantum mechanics, hydrogen emits a line spectrum.