Chapter 9 Atomic Structure

Chapter 9 Atomic Structure

Chapter 9 Atomic Structure
9.2 Wave Function and the Atomic Orbital 9.3 Electron Configurations and the Periodic Table 9.4 Trends in Some Key Periodic Atomic Properties

Key Points: To present the names and the allowed values and combinations of the quantum numbers To identify the principal energy levels within an atom and state the energy trend among them For each principal energy level (shell), state the number of subshells, identify them by letter, and state the energy trend among them To state the number of orbitals in each subshell

Key Points: To write the electron configuration of an element up to atomic number 36 To correlate the positions of the elements in the periodic table with the arrangement of electrons in each element To write valence electrons for each element To write the electron configuration of ions

Introduction Protons (P) Atomic nuclear Atom (A) Neutrons (N)
Electrons (Z) Charge Mass number Atomic number A=P+N=Z+N=atomic weights Atomic number = proton number = number of electrons

9. 2 Wave Function and Atomic Orbitals
De Broglie Relation Content :Matter, such as electrons, has both wave and particle properties. Expression λ = h/p = h/(mυ) DeBroglie (1924)

2. Heisenberg's Uncertainty Principle
Content It is impossible to determine accurately both the momentum and the position of an electron simultaneously. Expression (Δpx)(Δx) >h/4π Heisenberg, Werner 1901–76, German physicist 1932 Nobel Prize in physics

3.Wave Functions In 1926 Schrödinger developed a second-order partial-differential equation, from which we obtain a reasonable solution, ψ, the wave function, which square, ψ2, gives the probability of finding the particles within a region in the space. Schrödinger equation

Wave Functions Notice ψ is called the wave function, which is a solution of Schrödinger 's wave equation. ψ depends upon the coordinates x, y, and z. ψ has no simple physical meaning. ψ2 is the relative probability density of locating the particle at the position (x,y,z). So, ψ is a probability function.

What information about the position of a particle in a given state can we obtain if we know ψ for that state? If we know ψ， we can predict the probability of finding an electron in a particular region of space. There are many wave functions that are acceptable descriptions of the electron wave in an atom. Each of ψ is characterized by a set of quantum numbers (related to the shape and size of the electron wave and the location of the electron in three-dimensional space).

ψ for a given combination of n, l and m values is called an atomic orbitals.
ψ n , l , m (x,y,z) = atomic orbitals ※ ψ(wave function) = atomic orbitals (probability of finding an electron in a particular region of space) ψ n , l , m (x,y,z) = atomic orbitals

Principal Quantum Number—n
Symbol n Meaning n provides information about the distance of the electron from the nucleus and determines the energy of the electron mainly . Value n , 2, 3, 4, …n Shell letter K, L, M, N, … Notice

Orbitals of the same quantum state n are said to belong to the same shell.
In the case of the hydrogen atom or single-electron atomic ions, n is the only quantum number determining the energy. The smaller n is, the lower the energy.

Angular Momentum quantum number—l
Symbol l Meaning Each shell has one or more subshells. Orbitals of the same n but different l are said to belong to different subshells of a given shell. l describes the shape of the orbitals. Value l , 1, 2, 3, …(n-1) Subshell letter s, p, d, f, … Shape spherical, dumbbell, quincunx

For any value of n there are n sublevels.
Notice For any value of n there are n sublevels. If n=1(K shell), l =0(one sublevels)→1s→ If n=2(L shell), l =0 →2s→ l =1 →2p→ The energy of an electron in a many- electron atom depends on both n and l, therefore nl is referred as a level, such as 1s, 2s, 2p, etc. two sublevels

※For a given l, the energy of an orbital increases with n
※For a given l, the energy of an orbital increases with n. So, 1s<2s<3s <4s ※ For a given n, the energy of an orbital increases with l. So, ns<np<nd<nf. ※Orbitals of the different n and l, the ranges overlap. So, 4s < 3d.

Magnetic Quantum Number—m
Symbol m Meaning m distinguishes orbitals of given n and l but having a different orientation in space. Value m =0, ±1, ±2，…±l (a total 2l+1 values ) Notice The number of orbitals for each subshell is 2l+1 .

Subshell s p d Atomic Orbital shapes l = m = 1 0,+1,-1 2 0,+1,-1,+2,-2 number of orbitals 3 5 Orbital box diagrams All of the three different orbitals in a given p subshell have the same energy. degenerate orbitals

n 1 2 3 l 1 2 m +1, 0, -1 +2, +1, 0, -1,-2 Subshell (n) 1s 2s 2p 3s 3p 3d Number of orbitals(n2) 1 4 9 Energy levels(n) 1 2 3

ψ n , l , m (x,y,z) = atomic orbitals
The number of orbitals for each shell is n2 . shell subshell number of orbitals = n2 n= →s n= →s,p =4 n= →s,p,d =9 n= →s,p,d,f =16 The term atomic orbital refers to a wave function that has specified values of n, l, and m. ψ n , l , m (x,y,z) = atomic orbitals

Spin Quantum Number—ms
Symbol ms Meaning ms is used to describe the spinning electron. Value ms= ±1/2 or (↑and↓) Notice No more than two electrons can occupy the same atomic orbital if they have different spin quantum number .

No two electrons in an atom can have identical values of all four quantum.
The maximum number of electrons in each subshell=2(2l+1)= subshell capacity The maximum number of electrons in each energy level=2n2 =shell capacity In order to describe fully the state of an electron in an atom you must specify both its atomic orbital and its spin state, that is, you must specify the value of all four quantum numbers: n, l, m, and ms.

Summary describe fully the state of an electron → n, l, m, ms. describe atomic orbitals=wave functions ψ → n, l, m describe energy levels → n, l describe energy levels in hydrogen atom→ n n →shell l →subshell, shape of the orbitals, depend on n m → orientation of the orbitals, depend on l l=0 →s subshell→ spherical →1 orbital→2 electrons l=1 →p subshell→dumbbell→3 orbitals→6 electrons l=2 →d subshell→quincunx→5 orbitals→10electrons

Summary shell: number of orbitals= n2 energy levels=n maximum number of electrons=2n2 subshell: number of orbitals= 2l+1 energy levels=1 maximum number of electrons= 2(2l+1)

Example 1 What values of the angular momentum (l) and magnetic (m) quantum numbers are allowed for a principal quantum number (n) of 3?How many orbitals are allowed for n=3? Example 2 Give the notation used for each of the following subshells that is an allowed combination. If it is not an allowed combination, explain why. (a) n=2,l=0 (b) n=1,l=1 (c) n=4,l=2 (d) n=4,l=3

Example 3 State whether each of the following sets of quantum numbers is permissible for an electron in an atom. If a set is not permissible, explain why. (a) n = 1, l = 1, ml = 0, ms = +1/2 (b) n =3, l = 1, ml =-2, ms =-1/2 (c) n = 2, l = 1, ml = 0, ms = +1/2 (d) n = 2, l = 0, ml = 0, ms = 1

9.3 Electron Configurationgs and the Periodic Table
How do the electrons of a many-electron atom populate the available orbitals? Pauli Exclusion principle Building-Up Principle Hund's Rule

Pauli Exclusion principle
Content No two electrons in an atom can have the same four quantum numbers. An orbitals can hold at most two electrons, and then only if the electrons have opposite spins. Notice s2 , p6 , d10 , f14 . Two electrons in the same orbital must always have opposing spins, represented by "up" and "down" arrows.

The Electron Configurations and Orbital Diagrams

Example Which of the following orbital diagrams or electron configurations are possible and which are impossible, according to the Pauli exclusion principle? Explain. (d) ls3 2sl (a) ls 2s p (e) ls2 2s1 2p7 (b) ls 2s p (c) (f) ls2 2s2 2p6 3s2 3p6 3d8 4s2 ls 2s 2p

2. Building-Up Principle (Aufbau Principle)
A scheme used to reproduce the electron configurations of the ground states of atoms. Content The atomic orbitals are filled so that the total energy of all the electrons is minimized. Obtain the electron configuration of an atom by successively filling subshells in the following order: ls 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p

Order for increasing energy (important)
1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s … 33

Notice Write ground-state electron configurations of atoms Z = 1 to Z = 36. Remember that the number of electrons = the atomic number Z. hydrogen H ls1 helium He ls2 lithium Li ls2 2s1 beryllium Be ls2 2s2 boron B ls2 2s2 2p1 carbon C ls2 2s2 2p2 nitrogen N ls2 2s2 2p3

oxygen O ls2 2s2 2p4 fluorine F ls2 2s2 2p5 neon Ne ls2 2s2 2p6 sodium Na ls2 2s2 2p6 3s1 or [Ne] 3s1 magnesium 12Mg ls2 2s2 2p6 3s1 or [Ne] 3s2 aluminum Al [Ne] 3s2 3p1 silicon Si [Ne] 3s2 3p2 phosphorus 15P [Ne] 3s2 3p3 sulfur S [Ne] 3s2 3p4 chlorine Cl [Ne] 3s2 3p5 argon Ar ls2 2s2 2p6 3s2 3p6 potassium K [Ar] 4s1 gallium Ga [Ar] 3d10 4s2 4p1

Notice Write ground-state electron configurations of atoms Z = 1 to Z = 36. Remember that the number of electrons = the atomic number Z. hydrogen H ls1 helium He ls2 lithium Li ls2 2s1 beryllium Be ls2 2s2 boron B ls2 2s2 2p1 carbon C ls2 2s2 2p2 nitrogen N ls2 2s2 2p3

noble-gas core, pseudo-noble-gas core, and valence electron
Element Total Electron Configuration Core Electrons Valence Electrons Group 11Na [Ne]3s1 1s22s22p6 3s1 1A 14Si [Ne]3s23p2 3s23p2 ⅣA 23V [Ar]3d34s2 1s22s22p63s23p6 3d34s2 ⅤB 33As [Ar]3dl04s24p3 1s22s22p63s23p63d10 4s24p3 ⅤA valence electron: ns+np (n-1)d+ns

two Exceptions to the building-up principle: valence electron
chromium 24Cr [Ar] 3d5 4s1 [Ar] 3d4 4s2 copper Cu [Ar] 3d10 4s1 [Ar] 3d9 4s2 21 scandium Sc [Ar] 3d1 4s2 22 titanium Ti [Ar] 3d2 4s2 23 vanadium V [Ar] 3d3 4s2 24 chromium Cr [Ar] 3d5 4s1 25 manganese 25Mn [Ar] 3d5 4s2 26 iron Fe [Ar] 3d6 4s2 27 cobalt Co [Ar] 3d7 4s2 28 nickel Ni [Ar] 3d8 4s2 29 copper Cu [Ar] 3d10 4s1 30 zinc Zn [Ar] 3d10 4s2

17Cl [Ne] 3s2 3p5 + e- →Cl- [Ne] 3s2 3p6=[Ar]
atom→loss of valence electrons(n)→cations → a stable noble gas configuration atom→ addition of electrons to valence orbitals →anions → a stable noble gas configuration 11Na [Ne] 3s1→Na+ [Ne] + e- 17Cl [Ne] 3s2 3p5 + e- →Cl- [Ne] 3s2 3p6=[Ar] The ns electrons are lost before the (n - 1)d electrons. 26Fe [Ar]3d64s2→Fe2+[Ar]3d6 + 2e- Fe2+[Ar]3d6 →Fe3+[Ar]3d5 + e-

Example Use the building-up principle to obtain the configuration for the ground state of the gallium atom (Z = 31 ). Give the configuration in complete form (do not abbreviate for the core). What is the valence-shell configuration? How about germanium (Z = 32 ), arsenic (Z = 33 )，selenium (Z = 34 )，bromine (Z = 35 )，krypton (Z = 36 )？

How to write orbital diagrams of carbon atom (Z = 6) ?
Question: How to write orbital diagrams of carbon atom (Z = 6) ? chromium Cr [Ar] 3d5 4s1 copper Cu [Ar] 3d10 4s1 Carbon 6C ls s p2 Diagram 1: Diagram 2: Diagram 3:

3. Hund's rule Content The lowest energy arrangement of electrons in a subshell is obtained by putting electrons into separate orbitals of the subshell with the same spin before pairing electrons. In filling degenerate orbitals, one electron occupies each orbital and all have identical spins, before any two electrons are placed in the same orbital. carbon 6C ls2 2s2 2p2

Notice The total energy of all the electrons is minimized when a sublevel is half-filled or completely filled. chromium Cr [Ar] 3d5 4s1 copper Cu [Ar] 3d10 4s1 Magnetic Properties of Atoms paramagnetic → unpaired (one or more unpaired electrons) diamagnetic → paired (no unpaired electrons)

Example 1. Fill in the blanks. The electron configuration 3d7 indicates that there are electrons in the subshell, in the shell. "Electrons go into the lowest energy subshell" is a statement of the principle. "Electrons in the same orbital must be paired" is a statement of the principle. "Electrons go into separate orbitals with parallel spins" is a statement of

Example 2. (a) Write the electron configuration for the Co atom, using the noble gas notation. Then draw the orbital box diagram for the electrons beyond the preceding noble gas configuration. (b) Cobalt commonly exists as 2+ and 3 + ions. How does the orbital box diagram given in part (a) have to be changed to represent the outer electrons of Co2+ and Co3+? (c) How many unpaired electrons do Co, Co2+, and Co3+ have?

Procedure Find the atomic number List the subshells in order of increasing energy ls 2s 2p 3s 3p 4s 3d 4p Put electrons into subshells as superscripts until you reach the element in question. Add the superscripts and check the total against the atomic number. They should be equal. Write valence electrons (orbital diagram for the outer orbitals) and point out unpaired electrons . The electron configurations of ions are written by starting with the electron configuration of the atoms and then adding or removing the correct number of electrons.

Example 3. Write the electron configurations for sulfur (Z = 16), mercury(Z = 80) and silver (Z = 47), which is diamagnetic. 4. In each part identify the orbital diagram as the ground state, excited state, or an impossible state. If it is an impossible state tell why. ls 2s 2p (a) (b) (c)

9.4 Some Periodic Properties
Question: Why and how did the periodic table originate? What does electron configuration have to do with the periodic table? What kinds of groupings of elements are possible? What information about the elements does it so conveniently display?

Terms The periodic law: The periodic law states that when the elements are arranged by atomic number, their physical and chemical properties vary periodically. Period: Horizontal rows of elements in the table are called periods. Group: Families of elements fall into vertical columns called groups.

1. The Periodic Table Question Why and how did the periodic table originate? Period Energy Level Group and Period : the same integral number for (n+0.7l)→ the same energy level group → Period The period number=the maximum value of n in such a configuration

energy level group Orbitals Filled Period Number of electrons
Number of elements Ⅰ 1s 2 Ⅱ 2s 2p 8 Ⅲ 3s 3p Ⅳ 4s 3d 4p 18 Ⅴ 5s 4d 5p Ⅵ 6s 4f 5d 6p 32 Ⅶ 7s 5f 6d 7p short period short period short period long periods long periods long periods incomplete

Question What are some ways that elements can be classified or grouped? Group Valence Electrons and Group: the same number of valence electrons → group With the exception of groups VIIIB and IB and ⅡB, the group number= the number of valence electrons

ⅠB ⅡB ⅢB～ VIIIB (n-1)d10 ns1 (n-1)d10 ns2 (n-1)d1～8 ns1～2
The Main Group or Representative Elements ⅠA ⅡA ⅢA ⅣA ⅤA ⅥA ⅦA VIIIA nsl ns2 ns2np1 ns2np2 ns2np3 ns2np4 ns2np5 ns2np6 alkali metals alkaline earth metals chalcogens halogens Noble Gases The Transition Metals (Group B Elements) ⅠB ⅡB ⅢB～ VIIIB (n-1)d10 ns1 (n-1)d10 ns2 (n-1)d1～8 ns1～2

block 1 2 3 4 5 6 7 s block ns1~ns2 d block (n-1)d1~8ns2 ds block
IA VIIIA 1 2 3 4 5 6 7 IIA IIIA IVA VA VIA VIIA block IIIB IVB VB VIB VIIB VIIIB IB IIB s block ns1~ns2 d block (n-1)d1~8ns2 ds block (n-1)d10ns1~2 p block ns2np1~6 s-block elements ⅠA, ⅡA nsl ～2 metals p-block elements ⅢA～ VIIIA ns2 np1～6 nonmetals ds-block elements IB ～ IIB (n-1)d10ns1 ～2 d-block elements Ⅲ B ～ VIIIB (n-1)d1～8 ns2 f-block elements the lanthanide and actinide series

Write an element's valence electron configuration and give its position in the periodic table.
the period number=the maximum value of n in valence electron configuration the group number= the number of valence electrons(exception of VIIIB, IB, ⅡB) Example 1. What are the configurations for the outer electrons of (a) gallium, Z = 31, and (b) nickel, Z = 28? Give their position in the periodic table.

Example 2. A neutral atom of a certain element has 15 electrons. Without consulting a periodic table, answer the following questions: (a) What is the electron configuration of the element? (b) What are the valence electrons in the element? (c) Is the atom of this element diamagnetic or paramagnetic?

Example 3. Write the electron configuration for (a) all elements from lithium through neon that are not paramagnetic. (b) the element with the largest paramagnetism among the first 36 elements in the periodic table. (c) all elements with an atomic number less than 10 that have one unpaired electron.

2. Periodic Trends of the elements Atomic Radius
Definition The atomic radius of a metal is one-half the distance between the two nuclei in two adjacent atoms. For elements that exist as simple diatomic molecules, the atomic radius is one-half the distance between the nuclei of the two atoms in a particular molecule. r r

Atomic Radius Symbol r Conclusion The atomic radius generally decrease across a period and increase down a group. decrease The largest atom is Cesium. Increase

Conclusion: most electronegative (F) =4.0
Electronegativity Definition Electronegativity is a measure of the ability of an atom attracting the sharing electrons in a compound. Symbol X Conclusion: most electronegative (F) =4.0 X ( metals)<2, X (nonmetals)>2 Increase Electronegativity decrease

Chapter 9 Atomic Structure

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