Quantum-Mechanical Model of the Atom

1. Quantum-Mechanical Model of the Atom • Describes the probability that the electron will be in a certain region of space at a given instant. • Orbitals are regions of different energies where the electrons can be found.

2. The quantum-mechanical model uses 3 quantum numbers to describe an orbital: • The principal quantum number (n) • Can be any positive integer (n=1, n=2, n=3, etc.) • Describes the energy level

3. The angular momentum quantum number (l) Lowercase cursive L • Can have values from 0 to (n–1) • Defines the shape of the orbital • The magnetic quantum number (ml) • Can have integer values between – l and + l • Describes the orientation of the orbital in space

5. s orbitals Have a spherical shape. There is one orbital in each s subshell.

6. p orbitals Dumbbell shaped orbitals Each p subshell contains 3 orbitals. Each of the 3 orbitals is oriented along a different axis (x, y, or z)

7. d orbitals Each d sublevel contains 5 orbitals. 4 of the 5 orbitals have a four-leaf clover shape. The dz2 orbital has lobes on the z axis and a “doughnut” shape in the x-y plane.

8. f orbitals An f sublevel will contain 7 orbitals

9. All orbitals in the same subshell are said to be degenerate, meaning that they have the same energy. (i.e. the 3 orbitals in the 2p sublevel each have the same energy). • A maximum of 2 electrons can be located in a given orbital.

10. Subshells

11. The fourth quantum number • The magnetic spin quantum number (ms) • Can have a value of either + ½ or – ½ • Represents the electron’s spin about its axis, which can generate a magnetic field in two possible directions. • The Pauli Exclusion Principle • No two electrons in an atom can have the same quantum numbers. • Therefore two electrons found in the same orbital will have opposite spins (+ ½ and – ½)

12. Rules for writing electron configurations: • Aufbau Principle: orbitals are filled in order of increasing energy (lowest energy orbitals filled first). • Pauli Exclusion Principle: no more than two electrons can be found in a single orbital. Two electrons in the same orbital have opposite spins. • Hund’s Rule: for degenerate orbitals, the lowest energy is obtained when the number of electrons with the same spin is maximized.

16. Valence Electrons • outer-shell electrons • Include s and p electrons in the highest energy level • Electrons that are involved in chemical bonding • Core Electrons = inner-shell electrons • For example, a phosphorus atom has 15 total electrons • Phosphorus has 5 valence electrons (the electrons in the 3s and 3 p orbitals) • Phosphorus has 10 core electrons (found in the first and second energy levels)

17. The octet rule atoms tend to form chemical bonds to reach a full outer-shell of 8 valence electrons. • For example, the phosphorus atom on the previous slide would gain three electrons to reach a full outer shell. This P3- ion would have the same electron configuration as the element argon. • When an atom and an ion have the same electron configuration, they are said to be isoelectronic.

18. Transition metal ions • d and f electrons are not considered valence electrons. • Outer shell s and p electrons will be lost first. • For example: Fe Fe2+ Fe3+