Quantum Numbers and Atomic Orbitals - Chemistry 7 Numbers and Atomic Orbitals Each electron in an...

Quantum Numbers and Atomic Orbitals

Each electron in an atom can be described by 4

quantum numbers: n, l, ml, ms.

An orbital describes a region in space where an

electron is most probably located.

10 September 2013 1

Name Symbol Permitted Values Property

Principal n Positive integers Orbital

energy (size)

Angular

momentum

l Integers from 0 to

n-1

Orbital shape

(s/p/d/f)

Magnetic ml Integers from -l

to 0 to +l

Orbital

orientation in

space

Spin ms +1/2 or -1/2 Direction of

e- spin

Orbital Shapes

10 September 2013 2

A shell describes electrons with the

same value of n. A subshell refers to

specific n,l quantum number (example:

2s subshell, or 3p subshell).

3 10 September 2013

size shape orientation

Learning Check

What is wrong with the following quantum

number designations and/or sublevel names?

Supply the missing quantum numbers and

sublevel names.

4

n l ml Name

(a) 1 1 0 1p

(b) 4 3 +1 4d

(c) 3 1 -2 3p

If n=1, only l=0 exists

l=3 is an f sublevel

If l=1, ml cannot be -2

n l ml Name

(a) ? ? 0 4p

(b) 2 1 0 ?

(c) ? ? ? 2s

Special Case of the H Atom

The energy state of the H atom depends

only on the principal quantum number n.

10 September 2013 5

Chapter 8 Electron Configuration and Chemical Periodicity

Outline

1. Characteristics of Many-Electron Atoms

2. The Quantum-Mechanical Model and the

Periodic Table

3. Trends in Three Atomic Properties

4. Atomic Structure and Chemical Reactivity

10 September 2013 7

Excluded Topics:

• Trends among the transition elements

• Trends in electron affinity

• Pseudo-noble gas configuration

How does the distribution of electrons within the orbitals of an

element’s atoms relate to its chemical and physical properties?

Periodic Table

In 1870, Mendeleev arranged the 65

elements then known into a periodic table.

◦ Based on the periodic law: when the elements are

arranged in order of increasing atomic mass,

certain sets of chemical and physical properties

recur periodically

10 September 2013 8

Quantum Numbers and the

Exclusion Principle

Each electron in any atom is described

completely by a set of four quantum

numbers.

◦ The first three quantum numbers describe the

orbital, while the fourth quantum number

describes electron spin.

Pauli’s exclusion principle states that no

two electrons in the same atom can have the

same four quantum numbers.

An atomic orbital can hold a maximum of 2

e- and they must have opposing spins. 10 September 2013 9

Electronic Configuration

Distribution of electrons

within the orbitals

The lowest energy (ground

state) electronic

configuration of all elements

are constructed by filling

lowest energy orbitals

sequentially aufbau

principle

10 September 2013 11

Order of Filling the Orbitals

Memorize the order of filling orbitals! Use mnemonic device.

Recall: for an H atom, orbital energy depends on the quantum number n.

For many-electron atoms, orbital energy depends on both n and l (3s < 3p < 3d).


spdf Notation and Orbital

Diagrams

Used to denote the ground state

electronic configuration of elements


Element spdf

notation

Orbital box

diagram

H 1s1

He 1s2

n quantum #

l quantum #

# of e- in orbital

spin quantum

#: an arrow

denotes an

electron with

“spin up”

(ms=+1/2) or

“spin down”

(ms=-1/2)

Building Orbital Diagrams

1. Aufbau principle: electrons are always

placed in the lowest energy sublevel

available.

2. Exclusion principle: each orbital may

contain a maximum of 2 electrons, which

must have opposite spins.


H (Z = 1) 1s1

1s

↑

He (Z = 2) 1s2

1s

↑↓

Building Orbital Diagrams

3. Hund’s rule: when orbitals of equal

energy are available, the lowest energy

electron configuration has the maximum

number of unpaired electrons with

parallel spins.

15

N (Z = 7) 1s22s22p3

Learning Check

Write a set of quantum numbers for the 3rd e- and a set for the 8th e- of the F atom.

Use the periodic table to identify the element with the electronic configuration 1s22s22p4. Write its orbital diagram.


F (Z = 9) 1s22s22p3

For the 3rd electron: n = 2, l = 0, ml = 0, ms = +½

For the 8th electron: n = 2, l = 1, ml = -1, ms = -½

Partial Orbital Diagram and

Condensed Configurations

Partial orbital diagram: shows only the

highest energy sublevels being filled.

Condensed electron configuration: has

the element symbol of the previous

noble gas in square brackets


Al (Z = 13) 1s22s22p63s23p1 ↑↓

3s 3p

↑

Al has the condensed configuration [Ne]3s23p1

Learning Check

Full Electron

Configuration

Element Condensed

Electron

Configuration

Partial

Orbital

Diagram

1s22s22p63s1 Na [Ne]3s1

1s22s22p63s2 Mg [Ne]3s2

1s22s22p63s23p4 S [Ne]3s23p4

1s22s22p63s23p4 Cl [Ne]3s23p5


Electron Configuration and

Group

Elements in the same group:

◦ Have the same outer electron

configuration

◦ Exhibit similar chemical behavior

Similar outer electron

configurations correlate with

similar chemical behavior.


Learning Check

Write the full and

condensed electron

configuration of the

following elements:

◦ Ca (20)

◦ Ti (22)

◦ Mn (25)

◦ Ni (28)

◦ As (33)

◦ Kr (36)


Period 4 Elements


*Colored type indicates the sublevel to which the last electron is added.

Orbital Filling

and the Periodic Table


The order in which the orbitals are filled can be obtained directly

from the periodic table.

Announcements Quiz # 7 on Sept 17.

LT # 3 on Sept 26 Th 6-7:30 PM, Venue TBA.

Chapter 8 Problem Set: 8, 10, 19, 20, 21, 23, 25,

27, 29, 30, 31, 32, 36, 41, 45, 47, 53, 56, 57, 59,

61, 64, 65

Problem Solving Class Schedule:


Ch 7 D F 12:30 – 1:30 SOM 202

Ch 7 E F 11:30 – 12:30 CTC 102

Ch 7 F M 12:30 – 1:30 CTC 104

Ch 7 G W 2:30 – 3:30 SOM 105

Ch 7 H-K MWF 3:30 – 4:30 C 109

Ch 7 L T 4:30 – 5:30 C 114

Ch 7 C M 2:30-3:30 SOM 105

Quantum Numbers and Atomic Orbitals - Chemistry 7 Numbers and Atomic Orbitals Each electron in an...

Documents

Transcript of Quantum Numbers and Atomic Orbitals - Chemistry 7 Numbers and Atomic Orbitals Each electron in an...