Describe the Bohr model for the hydrogen atom.

Quantum theory is the theoretical basis of modern physics that explains the nature and behavior of matter and energy on the atomic and subatomic level. The core principle of quantum theory is that energy is not continuous, but rather comes in small but discrete units called quanta. The Bohr Model, introduced by Niels Bohr, incorporated quantum theory by suggesting that electrons can only exist in certain discrete orbits around the nucleus, each with a quantized amount of energy.

One of the startling conclusions of quantum theory is that particles such as electrons have properties of both particles and waves. This duality addresses the complex nature of how electrons behave and interact with energy — a concept that was refined and further developed in later quantum mechanics.

Energy levels are a fundamental concept when discussing the Bohr Model. These are the specific 'shells' or 'orbits' where electrons reside as they circle the nucleus. In Bohr's concept, these orbits are not arbitrary: each energy level corresponds to a specific amount of energy that an electron can possess while being part of an atom.

The energy levels are crucial to understanding how atoms absorb and emit light. As electrons move between these levels, they absorb or release precise amounts of energy, which correspond to specific wavelengths (or colors) of light. The quantized nature of these energy levels is what causes atoms to have unique spectral lines, as seen in emission or absorption spectra.

The principal quantum number, denoted by the symbol `n`, is central to the Bohr Model. It's a positive integer (n=1,2,3,...) that principally determines the size and energy of the orbital where an electron can be found. The energy associated with each orbital is determined by the formula \( E_n = -\frac{13.6 \text{ eV}}{n^2} \) where \( E_n \) is the energy of an electron at a particular energy level 'n'.

As 'n' increases, the energy levels become closer together, which means that the energies of the higher orbits are less negative and hence, the electron is less tightly bound to the nucleus. The principal quantum number also spheres a considerable influence on other properties of the electron, like angular momentum and orbital shape, which are further defined in advanced quantum mechanics.

Electron transitions are changes in the energy state of an electron within an atom. When an electron in the hydrogen atom jumps from a higher energy orbit to a lower one, it emits a photon — a particle of light — which carries the energy difference between the two orbits. Conversely, if an electron absorbs energy, it can be excited from a lower orbit to a higher one.

The emitted or absorbed energy is precisely quantified, and the relationship is described by the equation \( E = h u \) where \( E \) is the energy of the photon, \( h \) is Planck's constant, and \( u \) is the frequency of the photon. The specific colors of light emitted or absorbed are unique to each element, providing a fingerprint that can be used in techniques like spectroscopy to identify elements within a sample.