Electronic Structure of Atoms Ch. 7 (7.5-7.6) Quantum Numbers Electronic Structure of Atoms

Heisenberg Uncertainty Principle It is impossible to know exactly the location and velocity of a particle. The better we know one, the less we know the other; measuring changes the properties You can find out where the Electron is, but not where it is going. -OR- Electron is going, but not where it is!

Quantum Mechanics Erwin Schrödinger developed a mathematical treatment into which both the wave and particle nature of matter could be incorporated. It is known as quantum mechanics.

Quantum Mechanics The wave equation is designated with a lower case Greek psi (). The square of the wave equation, 2, gives a probability density map of where an electron has a certain statistical likelihood of being at any given instant in time.

According to the QM Model, each electron in an atom can be described by 4 quantum numbers (arrived at by solving Schrödingers equation) 3 specify the probability of finding the e- at various points in space (orbitals) 1 refers to the magnetic property of electrons QUANTUM ORGANIZATION Energy Level (shell) Sublevel (subshell) Atomic Orbital Spin

Principle Quantum Number, n The principal quantum number, n, describes the energy level (electron shell) on which the orbital resides. Maximum number of electrons = 2n2 As n increases: Size of electron shell increases Energy of electrons increases Distance between valence electrons and nucleus increases

Distributing Electrons in the Atom ENERGY LEVELS Energy Level Principal QN (n) Max. # of e- 1st 1 2(1)2 = 2 2nd 2 2(2)2 = 8 3rd 3 2(3)2 = 18 4th 4 2(4)2 = 32 5th 5 2(5)2 = 50 6th 6 2(6)2 = 72 7th 7 2(7)2 = 98

Angular momentum Quantum Number, l This quantum number defines the shape of the orbital /sublevel an electron is located in Also known as sublevel QN These shapes, according to Schrodinger’s wave equation, describe regions with high probability of finding electrons There are four types of orbitals

Distributing Electrons in the Atom Energy Level Principal QN (n) Max. # of e- (2n2) Sublevel (in each sublevel) 1st 1 2 s 2nd 8 s, p 2, 6 3rd 3 18 s, p, d 2, 6, 10 4th 4 32 s, p, d, f 2, 6, 10, 14 5th, 6th, and 7th EL’s also only contain s,p,d, and f sublevels

Magnetic Quantum Number, ml Each sublevel is made up of orbitals Orbital: 3-D shape which describes the region where an electron will most likely be found Describes the three-dimensional orientation of the orbital. Also known as orbital QN Each orbital can hold a maximum of 2 electrons Each pair will have a different orientation in space on any given energy level, there can be up to 1 s orbital, 3 p orbitals, 5 d orbitals, 7 f orbitals, etc.

Each pair will have a different orientation in space on any given energy level, there can be up to 1 s orbital, 3 p orbitals, 5 d orbitals, 7 f orbitals, etc Each sublevel contains a certain number of orbitals s has 1 orbital p has 3 orbitals d has 5 orbitals f has 7 orbitals Orbitals in each sublevel have different unique shapes “e- cloud” is a combination of all orbitals in an atom

Magnetic Quantum Number, ml Orbitals with the same value of n form a shell. Different orbital types within a shell are subshells.

s Orbitals Value of l = 0. Spherical in shape. Radius of sphere increases with increasing value of n

s Orbitals Observing a graph of probabilities of finding an electron versus distance from the nucleus, we see that s orbitals possess n−1 nodes, or regions where there is 0 probability of finding an electron.

p Orbitals Value of l = 1. Have two lobes with a node between them.

d Orbitals Value of l is 2. Four of the five orbitals have 4 lobes; the other resembles a p orbital with a doughnut around the center.

Neon atom

Energies of Orbitals For a one-electron hydrogen atom, orbitals on the same energy level have the same energy. That is, they are degenerate.

Energies of Orbitals As the number of electrons increases, though, so does the repulsion between them. Therefore, in many-electron atoms, orbitals on the same energy level are no longer degenerate.

Spin Quantum Number, ms In the 1920s, it was discovered that two electrons in the same orbital do not have exactly the same energy. The “spin” of an electron describes its magnetic field, which affects its energy.

Spin Quantum Number, ms This led to a fourth quantum number, the spin quantum number, ms. The spin quantum number has only 2 allowed values: +1/2 and −1/2.

Pauli Exclusion Principle No two electrons in the same atom can have exactly the same energy. For example, no two electrons in the same atom can have identical sets of quantum numbers.

Hund’s Rule “For degenerate orbitals, the lowest energy is attained when the number of electrons with the same spin is maximized.”