Quantum Theory and the Atom

Learning Objective Describe the relationship between electron levels, sublevels and atomic orbitals.

Real-World Link A house number is not enough to deliver a letter to the correct address. More information, such as a street name, city, and state, is necessary to deliver the letter. Similarly, chemical elements are identified according to details about the arrangement of their electrons.

Bohr’s Model of the Atom Bohr suggested that electrons are arranged in concentric circular orbits around the nucleus.

Heisenberg’s Uncertainty Principle Heisenberg’s uncertainty principle – states that it is impossible to know both the momentum and position of an electron at the same time. In other words, it is impossible to know the exact location of an electron.

Heisenberg’s Uncertainty Principle The Heisenberg uncertainty principle means that it is impossible to assign fixed paths for electrons like the circular orbits in Bohr’s model. The only quantity that can be known is the probability for an electron to occupy a certain region around the nucleus.

Quantum Mechanical Model of the Atom Like Bohr’s model, the quantum mechanical model limits an electron’s energy to certain values. Unlike Bohr’s model, the quantum mechanical model does not attempt to describe the electron’s path around the nucleus.

Electron’s Probable Location Schrodinger’s wave function (an equation that treated the hydrogen atom electron as a wave) predicts a three- dimensional region around the nucleus, called an atomic orbital, which describes the electron’s probable location. An orbital can hold up to two electrons.

Quantum Numbers and Atomic Orbitals A set of four quantum numbers is needed to describe an electron’s location/properties within an atom. – Principal quantum number (n) – Orbital angular momentum quantum number (l) – Magnetic quantum number (m l ) – Electron spin quantum number (m s )

Principal Quantum Number The principal quantum number (n) describes the average distance of the orbital from the nucleus—and the energy of the electron in an atom. – It can only be a positive integer (whole number): n = 1, 2, 3, 4, 5… The larger the value of n, the higher the energy and the larger the orbital.

Principal Quantum Number n specifies the atom’s major energy levels Each major energy level is called a principal energy level or energy level.

Orbital Angular Momentum Quantum Number The orbital angular momentum quantum number (l) determines the shape of an orbital. Within each energy level, electrons are further grouped into energy sublevels.

Energy Sublevels Sublevels are labeled s, p, d, and f according to the shapes of the atom’s orbitals. S sublevel – spherical (has 1 orbital) P sublevel – dumbbell- shaped (has 3 orbitals) Not all d or f sublevels have the same shape – d sublevel has 5 orbitals – f sublevel has 7 orbitals

Magnetic Quantum Number The magnetic quantum number (m l ) describes how the various orbitals are oriented in space. – Orbitals can be oriented along x, y, and z axes. – Examples: 2p x, 2p y, 2p z

Electron Spin Quantum Number The electron spin quantum number (m s ) describes the direction the electron is spinning, either clockwise or counterclockwise. The two possible values of the spin quantum number are + ½ and - ½.

Level 2 Level 3 Level 4 4 sublevels Level 1 3 sublevels 2 sublevels 1 sublevel 1s (2 electrons) 2s (2 electrons) 4s (2 electrons) 4d (10 electrons) 2p (6 electrons) 4p (6 electrons) 4f (14 electrons) 3d (10 electrons) 3p (6 electrons) 3s (2 electrons)

Summary Bohr’s atomic model attributes hydrogen’s emission spectrum to electrons dropping from higher-energy to lower-energy orbits. The quantum mechanical model assumes that electrons have wave properties. Electrons occupy three-dimensional regions of space called atomic orbitals.