Summary of Bohr and QM Models

Chem 1115 students should be familiar with the concepts presented in class regarding the Bohr and Quantum Mechanical models of the atom. The following summary may be useful as you study for your Unit 6 exam.

The Bohr Model

• Bohr developed a model of the hydrogen atom that explained its line spectrum.

• In this model, the electron can occupy certain well-defined orbits around the nucleus. In other words, the location of the electron can be determined with certainty.
• The radius of the lowest orbit in this model is 0.529 angstroms. In other words, the electron of a hydrogen in its ground state (lowest energy level) would be found in a circular orbit 0.529 angstroms from the nucleus.

• The energy of a H atom depends on its principal quantum number, n, where n has integral values of 1, 2, 3, ….

• Each value of n corresponds to a different energy, E_n (i.e. energy is quantized)

• The energy of a given level, E_n , increases as n increases.

• Energy is emitted when an electron moves from one allowed circular orbit (a higher energy state) to another circular orbit of lower energy.

D E = E_final - E_initial = hu

• Bohr’s model only works for atoms or ions containing a single electron.

Summary of the Quantum Mechanical Model of the Atom

• In this model, electrons have a dual nature—both particle-like and wave-like properties.
• The behavior of an electron in an atom is described by solutions to the Schroedinger equation called wave functions (y).
• The allowed wave functions for an atom are commonly called orbitals.

• Each orbital has a specific energy, but the location of the electron in the atom is not known for certain (Heisenberg Uncertainty Principle).

• The probability of finding an electron at a given point in space is given by y ², the probability density.

• The energy, shape, and orientation in space of an orbital are described using three quantum numbers, n, l, and m_l.
• The principal quantum number, n, describes the energy of an orbital.
• The azimuthal or angular momentum quantum number, l, describes the shape of an orbital.
• The magnetic quantum number, m_l, describes the orientation in space of the orbital.

• Only certain combinations of quantum numbers are allowed. (You must be able to recognize allowed sets of quantum numbers!!)
• The Pauli Exclusion Principle tells us that each electron in an atom must have a unique set of quantum numbers. To accomplish this, a fourth quantum number, the electron spin quantum number(m_s) is added to the other three quantum numbers to describe an electron in an orbital.
• Hund’s Rule tells us that the lowest energy for an atom is obtained when the number of electrons that are unpaired in orbitals with the same energy is maximized. In other words, if more than one orbital in a subshell is available, electrons will enter an unfilled orbital first. For example, if electrons are being added into the three 2p orbitals, 1 electron should be placed in each of the 2p orbitals before pairing any electrons in the same 2p orbital.