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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 :.

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Chapter 9 Atomic Structure

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  1. Chapter 9 Atomic Structure

  2. 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

  3. 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

  4. 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

  5. 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

  6. 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)

  7. 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, Werner1901–76, German physicist1932 Nobel Prize in physics

  8. 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

  9. 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.

  10. 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).

  11. 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

  12. Principal Quantum Number—n • Symbol n • Meaningn provides information about the distance of the electron from the nucleus and determines the energy of the electron mainly . • Value n 1, 2, 3, 4, …n • Shell letter K, L, M, N, … • Notice

  13. 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.

  14. 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. • Valuel 0, 1, 2, 3, …(n-1) • Subshell letter s, p, d, f, … • Shape spherical, dumbbell, quincunx

  15. 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

  16. ※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.

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

  18. All of the three different orbitals in a given p subshell have the same energy. degenerate orbitals

  19. n 1 2 3 l 0 0 1 0 1 2 m 0 0 +1, 0, -1 0 +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

  20. The number of orbitals for each shell is n2 . • shell subshell number of orbitals = n2 • n=1 1→s 1 • n=2 2 →s,p 1+3=4 • n=3 3 →s,p,d 1+3+5=9 • n=4 4 →s,p,d,f 1+3+5+7=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

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

  22. 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.

  23. 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

  24. 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)

  25. 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

  26. 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

  27. 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

  28. 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.

  29. The Electron Configurations and Orbital Diagrams

  30. 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 2p (e) ls2 2s1 2p7 (b) ls 2s 2p (f) ls2 2s2 2p6 3s2 3p6 3d8 4s2 (c) ls 2s 2p

  31. 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

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

  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 1H ls1 • helium2He ls2 • lithium 3Li ls2 2s1 • beryllium 4Be ls2 2s2 • boron 5B ls2 2s22p1 • carbon 6C ls2 2s22p2 • nitrogen 7N ls2 2s22p3

  34. oxygen8O ls2 2s22p4 fluorine 9F ls2 2s22p5 neon 10Ne ls2 2s22p6 sodium 11Na ls2 2s22p6 3s1 or [Ne] 3s1 magnesium 12Mg ls2 2s22p6 3s1 or [Ne] 3s2 aluminum 13Al [Ne] 3s2 3p1 silicon 14Si [Ne] 3s2 3p2 phosphorus 15P [Ne] 3s2 3p3 sulfur 16S [Ne] 3s2 3p4 chlorine 17Cl [Ne] 3s2 3p5 argon 18Ar ls2 2s22p6 3s2 3p6 potassium 19K [Ar] 4s1 gallium 31Ga [Ar] 3d10 4s2 4p1

  35. Notice • Write ground-state electron configurations of atoms Z = 1 to Z = 36. Remember that the number of electrons = the atomic number Z. • hydrogen 1H ls1 • helium2He ls2 • lithium 3Li ls2 2s1 • beryllium 4Be ls2 2s2 • boron 5B ls2 2s22p1 • carbon 6C ls2 2s22p2 • nitrogen 7N ls2 2s22p3

  36. valence electron:ns+np (n-1)d+ns • noble-gas core, pseudo-noble-gas core, and valence electron

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

  38. 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-

  39. 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 )？

  40. Diagram 1: Diagram 2: Diagram 3: • Question: • How to write orbital diagrams of carbon atom (Z = 6) ? • chromium 24Cr [Ar] 3d5 4s1 • copper 29Cu [Ar] 3d10 4s1 Carbon 6C ls2 2s22p2

  41. 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 2s22p2

  42. Notice • The total energy of all the electrons is minimized when a sublevel is half-filled or completely filled. • chromium 24Cr [Ar] 3d5 4s1 • copper 29Cu [Ar] 3d10 4s1 • Magnetic Properties of Atoms • paramagnetic → unpaired (one or more unpaired electrons) • diamagnetic → paired (no unpaired electrons)

  43. Example 1. Fill in the blanks. The electron configuration 3d7 indicates that there areelectrons in thesubshell, in theshell. "Electrons go into the lowest energy subshell" is a statement of theprinciple. "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.

  44. 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?

  45. 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.

  46. 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)

  47. 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?

  48. 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.

  49. 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

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