Explain the difference between a Bohr orbit and a quantummechanical orbital.

The Bohr model, named after Niels Bohr, was a pioneering theory in atomic structure that presented electrons as having fixed orbits around the nucleus, akin to the way planets orbit the sun. It introduced the concept of quantized energy levels, with electrons circling at certain distances from the nucleus depending on their energy state. What made this model significant was the idea that electrons could jump between energy levels, emitting or absorbing discrete amounts of energy, or quanta, in the process.

Each orbit is designated with a principal quantum number, 'n', with the lowest energy level being n=1. Think of these orbits like the rungs of a ladder that an electron can move up or down, but not reside in between - a visualization that simplified complex atomic behaviors for early researchers. However, despite its success in explaining the hydrogen atom spectrum, the Bohr model has limitations. Mainly, it can't accurately predict phenomena in atoms with more than one electron due to the electron-electron interactions that the model doesn't take into account.

Quantum mechanics revolutionized the field of physics by introducing a framework for understanding the behavior of particles at the atomic and subatomic levels. It differs from classical physics, which can't adequately explain phenomena at the nanoscale. Quantum mechanics uses mathematical functions known as wavefunctions to describe the probabilities of finding an electron in a certain area. This probabilistic nature replaces the deterministic orbits of the Bohr model.

Where the Bohr model falls short, quantum mechanics excels. It can describe the behavior of electrons in all atoms, accounting for the strange dual nature of particles acting as both waves and particles, a concept that's integral to quantum theory. It allows for the description of electron behavior with a level of precision that matches experimental data, even for complex, multi-electron atoms.

Electron energy levels refer to the distinct energy states that an electron in an atom can occupy. In the Bohr model, these levels correspond to the fixed orbits around the nucleus. However, in the realm of quantum mechanics, energy levels are associated with specific quantum mechanical orbitals. Each energy level can house a set number of electrons, which determines the chemical properties of an element.

As electrons transition between these levels, they absorb or emit photons with energy equal to the difference between the levels involved. These transitions are responsible for the atomic emission spectra that are unique to each element. The concept of energy levels is crucial in understanding chemical bonding, the absorption and emission of light, and the electronic configuration of atoms.

Quantum numbers are the addresses of electrons, providing vital information about their position and behavior within the atom. There are four quantum numbers: the principal (n), the azimuthal (l), the magnetic (m_l), and the spin (m_s).

The principal quantum number, 'n', indicates the energy level and, in the Bohr model, the size of the orbit. The azimuthal quantum number, 'l', determines the shape of the orbital, which can be spherically shaped like a ball (s-orbitals) or dumbbell-shaped like a weight (p, d, and f orbitals). The magnetic quantum number, 'm_l', specifies the orientation of the orbital in three-dimensional space, and the spin quantum number, 'm_s', gives the direction of the electron's spin, either up or down. Together, these numbers define the probability of finding an electron in a given space within the atom, refining our understanding of electron configuration and atomic structure vis-a-vis quantum mechanics.