The Quantum View of the Atom Vocabulary: Heisenberg Uncertainty Principle radial probability distribution shell (energy level) orbital (subshell) s, p, d, and f “Under the Wave off Kanagawa”, Katsushika Hokusai, 1829

What was wrong with Bohr’s model? Only worked for hydrogen Violated Heisenberg’s uncertainty principle Where’s the love?

Heisenberg Uncertainty Principle You can not know both the position and the energy of an electron simultaneously.

Schrodinger and Probability Erwin Schrodinger solved the problem by developing “probability waves” using his wave equation. Probability wave: given an electron’s energy, Schrodinger’s wave equations identify the probable location of that electron. I hope no one asks me to explain that!

Probability Waves We represent probability waves as graphs (called radial probability distributions) of the probable location of an electron in its ground state around the nucleus of an atom. These graphs are interpreted as orbitals or subshells. Orbitals (subshells) have various shapes and exist on energy levels called shells.

Quantum Numbers The energy level (shell) that an electron occupies is called the principle quantum number (n). n can equal 1, 2, 3, … n=1 means the electron is on the 1st energy level, n=2 means the electron is on the 2nd energy level, etc.

Quantum Numbers Within each shell (energy level) there are subshells that the electrons can occupy. Subshells are also called orbitals. The subshell an electron occupies is called the Azimuthal quantum number and is assigned a letter: s, p, d, and f.

Types of orbitals (subshells) The “s” orbital ( only one type) s can orbitals exist on: n = 1 n = 2 n = 3 n = 4 n = 5 n = 6 n = 7 s orbitals on higher energy levels are larger

Types of orbitals The “s” orbital radial probability distribution: distance from nucleus (Å) 1s orbital Probability distance from nucleus (Å) 2s orbital

Types of orbitals The 1s, 2s, and 3s orbital radial probability distributions:

Types of orbitals The “p” orbitals (three types) p orbitals can exist on: n = 2 n = 3 n = 4 n = 5 n = 6 n = 7 p orbitals on higher energy levels are larger

Types of orbitals The “p” orbitals (three types) all three p orbitals exist simultaneously

Types of orbitals The “p” orbitals radial probability distribution:

Types of orbitals The 2p and 2s orbital radial probability distributions in an atom:

Types of orbitals The “d” orbitals (five types): d orbitals can exist on: n = 3 n = 4 n = 5 n = 6 n = 7 d orbitals on higher energy levels are larger

Types of orbitals The “d” orbitals (all together)

Types of orbitals The 3d, 3p, and 3s orbital radial probability distributions:

Types of orbitals The “f” orbitals (7 types): d orbitals can exist on: f orbitals on higher energy levels are larger

Shortcut On any energy level, n2 orbitals can exist: n=1: s (12 = 1, so only one orbital) n=2: s, px, py, and pz (22 = 4, so 4 orbitals) n=3: s, px, py, pz, dxy, dxz, dyz, dz2, and dx2-y2 (32 = 9, so 9 orbitals) n=4: s, px, py, pz, dxy, dxz, dyz, dz2, dx2-y2, and 7 f orbitals (42 = 16, so 16 orbitals)

This is why you learned my model first! So…. All of these orbitals exist simultaneously. This is why you learned my model first! But it was wrong!!