1. Atomic Structure – Atom Structure Chapter 4B

2. Quantum Numbers • As scientists learned more about atoms, they realized that they can find the probably location of each electron in the ground state by using an four part address • Ground state is the lowest energy position • Each part of the address is determined by a Quantum Number • Principle Quantum Number (n) • Azimuthal Quantum Number (l) • Magnetic Quantum Number (m) • Electron-Spin Quantum Number (ms) • Quantum numbers are solutions to various wave equations used to describe energy, momentum, and probable locations of an electron

3. Address Location #1 • Principle Quantum Number (n) • Identifies the principle energy level • This number indicates the average or most likely distance from the nucleus where an electron resides. • Principle Quantum numbers are positive integers beginning at 1. • The highest value of (n) for large atoms in the ground state is 7 • If the atom is excited, it can be much higher.

4. Address Location #2 • Azimuthal Quantum Number (l) • Within each principle energy level, electrons have greater probability of being found in certain regions called sublevels. • Azimuthal Quantum Numbers are positive integers solving for angular momentum. • Azimuthal Quantum Numbers, or sub-orbitals, are symmetrical shapes arranged around the nucleus in orientation determined by the azimuthal quantum number. • For any principle energy level (n), sub-levels (l) can have any integer value from 0 to n-1 • The four energy sublevels assigned (l) values of 0 thru 3 have been assigned the letters to avoid confusion.

5. Allowed Azimuthal Quantum Numbers for Each Principal Energy Level

6. Address Location #3 • Magnetic Quantum Number (m) • Magnetic quantum numbers describe the spatial orientation of the orbital within an atom • It is also called the orbital quantum number • For each sublevel there are 2l + 1 possible orbitals. • For example the third principle energy level (n=3), and in the third sublevel (l=2), there are 2(2) +1 = 5 orbitals where electrons can reside. • Every atom in their ground state with 3 or more primary energy level

7. Address Location #4 • Electron-Spin Quantum Number • Each orbital can hold only 2 electrons • These 2 electrons have opposite reactions to magnetic fields • Each of the 2 possible values are represented but an up half-arrow and a down half-arrow but since I can’t find the half-arrow symbol I will use the regular up arrow. • The Pauli exclusion principle says that since each electron must have different m values, not 2 electrons can have the same set of quantum numbers. • So electrons in the same orbital have different spins.

8. Sublevels and Orbitals • Each orbital has a distinctly shaped probability region identified by the letters: s, p, d, f, g, h, i, ….etc. • The s sublevel • The simplest suborbital • The s suborbital has a spherical shape • Unlike other sub-orbitals it contains only 1 orbital • So it is often called the s orbital as well • Every energy level has one “s” sublevel that contains one “s” orbital • Remember an orbital can only contain 2 electrons

9. Sub-levels and Orbitals • The p sublevel • The probability plot of the p sublevel consists of 3 dumbbell shaped orbitals arranged symmetrically around a three dimensional x-y-z graph. • 1 lies on the x-axis • 1 lies on the y-axis • 1 lies on the z-axis • Elements in their ground state with 2 or more primary energy levels has a p sublevel • 2 electrons of opposite spin can occupy each orbital so a p sublevel can hold a maximum of 6 electrons

10. Sub-levels and Orbitals • The d sublevel • The probability plot of the d sublevel consists of 5 orbitals oriented as shown. • Every element in their ground state with 3 or more primary energy levels have a d sublevel • A d sublevel may contain up to 10 electrons

11. Sub-levels and Orbitals • The f sublevel • The probability plot of the f sublevel consists of 7 possible orbitals. • Only ground state atoms with 4 or more energy levels have an f sublevel. • An f sublevel may contain up to 14 electrons • You may have noticed that some orbitals overlap – this is because the orbitals indicate probability areas. • The combination of the orbitals produces a roughly spherical region around the atom

12. Energy Levels and Occupied Sublevels

13. Relative Energies of Sublevels • Principle energy levels become larger in size as their energy level number increases • Sublevels are also ranked by their relative energies • The 1s sublevel has the least energy and is closest to the nucleus • The 2s2p sublevel have more energy since they are in the second principle energy level • The 2s sublevel has less energy than the 2p sublevel • All 3 orbitals in the 2p sublevel has the same relative energy

14. Relative Energies of Sublevels • Next higher in energy are the 3s3p sublevel. • Given the pattern you would expect that 3d would be the next higher sublevel, however this is not the case. • Instead the 4s is the next sublevel filled • This break in order is confusing but if we use the diagonal rule it will help you remember the order

15. Electron Configuration and the Periodic Table • The periodic table is organized by the electron configuration of the elements. • Atomic numbers increase from left to right across each row • Each row corresponds to the highest primary energy level for any given element. • Certain regions, or blocks, of the table indicate the sublevel to which the electrons are added.

17. Electron Configurations • Since the period table is organized by increasing atomic number, and the atomic number corresponds to the number of protons, we can use that atomic number to determine the total number of electrons in a neutral atom. • The Aufbau Principle states that arrangement of electrons in an atom is determined by adding electrons to an atom with a lower atomic number.

18. Orbital Notation • Orbital notation can be used to illustrate the electron configuration of an atom • Orbital notation consists of a horizontal line representing the orbital above which the orbital name is written. • The 2 electrons that occupy the sublevel are written by a half arrow up (representing spin quantum number ms = +1/2) and half arrow down (representing spin quantum number ms = -1/2)

19. Electron Configuration • Lets practice writing elements in the electron configuration • Hydrogen (Z=1) • Hydrogen has 1 electron so its electron configuration is written as : 1s1 • Helium has 2 electrons so its electron configuration is written as: 1s2 • Lithium has 3 electrons. It is also the first element in the 2nd row so its electron configuration is: 1s22s1 this can also be written as [He]2s1 • This is also sometimes called the noble gas notation

20. Electron Configuration • Once we get up to atoms with a few more electrons we hit another question • Consider the element Nitrogen (Z-7) • Nitrogen has 7 electrons as we start filling the electron configuration we encounter a problem • The first 4 electrons fill fine then we hit the p sublevel that has 3 different compartments each that hold 2 electrons. So which one fills first? • Hund’srule states that as electrons fill a sublevel, all orbitals receive one electron with the same spin before they pair up

21. Rules for “filling” energy levels • Electrons enter the lowest principal energy level available • Within a principal energy level: electrons enter the lowest energy sublevel available – Aufbau Principle • Within a sublevel: electrons enter each orbital one electron at a time until all orbitals have one electron. Then additional electrons enter each orbital until 2 electrons are in each orbital. Once all orbitals in a sublevel are filled, then the next electron enters the next higher energy sublevel. – Hund’sRule