Quantum Numbers 3.7 Quantum numbers are required to describe the distribution of electron density in an atom. There are three quantum numbers necessary to describe an atomic orbital. The principal quantum number (n) – designates size The angular moment quantum number (l) – describes shape The magnetic quantum number (ml) – specifies orientation

Quantum Numbers The principal quantum number (n) designates the size of the orbital. Larger values of n correspond to larger orbitals. The allowed values of n are integral numbers: 1, 2, 3 and so forth. The value of n corresponds to the value of n in Bohr’s model of the hydrogen atom. A collection of orbitals with the same value of n is frequently called a principle energy level or shell.

The allowed values of l range from 0 to n – 1. Quantum Numbers The angular moment quantum number (l) describes the shape of the orbital. The values of l are integers that depend on the value of the principal quantum number The allowed values of l range from 0 to n – 1. Example: If n = 2, l can be 0 or 1. A collection of orbitals with the same value of n and l is referred to as a subshell. l 1 2 3 Orbital designation s p d f

Quantum Numbers The magnetic quantum number (ml) describes the orientation of the orbital in space. The values of ml are integers that depend on the value of the angular moment quantum number: – l,…0,…+l

Quantum Numbers Quantum numbers designate shells, subshells, and orbitals.

Worked Example 3.8 What are the possible values for the magnetic quantum number (ml) when the principal quantum number (n) is 3 and the angular quantum number (l) is 1? Strategy Recall that the possible values of ml depend on the value of l, not on the value of n. Setup The possible values of ml are – l,…0,…+l. Text Practice: 3.81 3.82

Quantum Numbers The electron spin quantum number (ms ) is used to specify an electron’s spin. There are two possible directions of spin. Allowed values of ms are +½ and −½.

Quantum Numbers A beam of atoms is split by a magnetic field. Statistically, half of the electrons spin clockwise, the other half spin counterclockwise.

2px Quantum Numbers To summarize quantum numbers: principal (n) – size angular (l) – shape magnetic (ml) – orientation electron spin (ms) direction of spin Required to describe an atomic orbital principal (n = 2) 2px related to the magnetic quantum number (ml ) angular momentum (l = 1) Required to describe an electron in an atomic orbital

Atomic Orbitals 3.8 All s orbitals are spherical in shape but differ in size: 1s < 2s < 3s principal quantum number (n = 2) 2s angular momentum quantum number (l = 0) ml = 0; only 1 orientation possible

l = 1 (as required for a p orbital) Atomic Orbitals The p orbitals: Three orientations: l = 1 (as required for a p orbital) ml = –1, 0, +1

l = 2 (as required for a d orbital) Atomic Orbitals The d orbitals: Five orientations: l = 2 (as required for a d orbital) ml = –2, –1, 0, +1, +2 http://mw.concord.org/modeler/showcase/simulation.html?s=http://mw2.concord.org/public/student/quantumchemistry/atomicorbitals.html

Energies of Orbitals The energies of orbitals in the hydrogen atom depend only on the principal quantum number. 3s subshell (n = 3; l = 0) 3rd shell (n = 3) 3p subshell (n = 3; l = 1) 3d subshell (n = 3; l = 2) 2s subshell (n = 2; l = 0) 2nd shell (n = 2) 2p subshell (n = 2; l = 1)

Worked Example 3.9 List the values of n, l, and ml for each of the orbitals in a 4d subshell. Strategy Consider the significance of the number and the letter in the 4d designation and determine the values of n and l. There are multiple values for ml, which will have to be deduced from the value of l. Text Practice: 3.86 3.90

Study Guide for sections 3.7-3.8 DAY 6, Terms to know: Sections 3.7-3.8 quantum numbers, orbitals, Pauli exclusion principle DAY 6, Specific outcomes and skills that may be tested on exam 1: Sections 3.7-3.8 Given a set of quantum numbers, be able to describe the energy level, subshell (s, p, d, or f), and spin state for an electron Given information about the principle energy level or shell, subshell (s, p, d, or f), and orbital, be able to determine a set of 4 possible quantum numbers for an electron Be able to recognize that no two electrons in the same atom can have the same values for each of the 4 quantum numbers Be able to describe an experiment that could be used to show that half of the electrons in an atom have a spin = ½ and the other half have a spin = -½. Be able to draw a figure that shows the shape and location of nodes in any orbital in the 1st, 2nd, or 3rd energy level of an atom Be able to rank the relative energies of any two orbitals in the 1st, 2nd, or 3rd energy levels of an atom and explain WHY

Extra Practice Problems for sections 3.7-3.8 Complete these problems outside of class until you are confident you have learned the SKILLS in this section outlined on the study guide and we will review some of them next class period. 3.75 3.77 3.83 3.85 3.89 3.123

Prep for day 7 Must watch videos: Other helpful videos: http://www.learnerstv.com/video/Free-video-Lecture-3349-Chemistry.htm (electron configurations) http://www.learnerstv.com/video/Free-video-Lecture-3350-Chemistry.htm (more on electron configurations) http://www.learnerstv.com/video/Free-video-Lecture-3351-Chemistry.htm (more electron configuration examples) Other helpful videos: http://echem1a.cchem.berkeley.edu/modules/module-3/ (UC-Berkeley watch lesson 8) http://ocw.mit.edu/courses/chemistry/5-111-principles-of-chemical-science-fall-2008/video-lectures/ (MIT lecture 8) Read sections 3.9-3.10 We will review for exam 1 during the next class, so practice as many example problems from chapters 1-3 as you can before then so you can ask questions about them in the next class period.