1 Periodicity & Atomic Structure Chapter 5

2 The Periodic Table01 The periodic table is the most important organizing principle in chemistry. Chemical and physical properties of elements in the same group are similar. All chemical and physical properties vary in a periodic manner, hence the name periodic table.

3 Development of the Periodic Table Mendeleev’s Periodic Table (1871) Until the discovery of the proton, the elements were typically organized by increasing atomic weight. The modern organization is by increasing atomic number.

4 The Periodic Table04 Ar = amu, would appear on the right of K = amu

Development of Modern Periodic Table In 1913 Moseley discovered that when elements were irradiated with high energy radiation y emitted X-ray. He used the frequency of the emitted radiation to calculate the atomic number. √ υ = a( Z-b)

6 The Periodic Table03

8 What is light made of ? 1) Made of Waves? Waves interfere,WavesWaves interfere, 2) Made of particles? 3) Made of both? 4) What are electron’s made of?

9 Electromagnetic Radiation02

10 Electromagnetic Radiation01 Frequency (, Greek nu): Number of peaks that pass a given point per unit time. Wavelength (, Greek lambda): Distance from one wave peak to the next. Amplitude: Height measured from the center of the wave. The square of the amplitude gives intensity.

11 Electromagnetic Radiation03

12 Electromagnetic Radiation04 Speed of a wave is the wavelength (in meters) multiplied by its frequency (in reciprocal seconds, (s –1 ) ). – Wavelength x Frequency = Speed – (m) x (s –1 ) = c (m/s)

13 Learning Check The red light in a laser pointer comes from a diode laser that has a wavelength of about 630 nm. What is the frequency of the light? C = x 10 8 m.s –1

14 x = c = c/ = x 10 8 m/s / 6.0 x 10 4 Hz = 5.0 x 10 3 m Radio wave A photon has a frequency of 6.0 x 10 4 Hz (s -1 ). Convert this frequency into wavelength (nm). Does this frequency fall in the visible region? = 5.0 x nm c = x 10 8 m/s –1

15 Atomic Spectra01 Atomic spectra: Result from excited atoms emitting light. Line spectra: Result from electron transitions between specific energy levels.

16 Maxwell (1873), proposed that visible light consists of electromagnetic waves. Electromagnetic radiation is the emission and transmission of energy in the form of electromagnetic waves. Speed of light (c) in vacuum = 3.00 x 10 8 m/s All electromagnetic radiation x  c 7.1 c = x 10 8 m/s –1

Line Emission Spectrum of Hydrogen Atoms

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19 “Photoelectric Effect” h KE e - Depending on metal used only lights of certain minimum frequency could cause ejection of electron Light must be composed of particles called photon Light has both: 1.wave nature 2.particle nature Planks and Einstein

20 Particle like Properties of Electromagnetic Energy

21 Planck in 1900 Energy (light) is emitted or absorbed in discrete units (quantum). E = h x Planck’s constant (h) h = 6.63 x J s

22 “Photoelectric Effect”

23 Light has both: 1.wave nature 2.particle nature “Photoelectric Effect” Solved by Einstein in 1905 Photon is a “particle” of light h KE e -

24 1.e - can only have specific (quantized) energy values 2.light is emitted as e - moves from one energy level to a lower energy level Bohr’s Model of the Atom (1913) E n = -R H ( ) 1 n2n2 n (principal quantum number) = 1,2,3,… R H (constant) = 2.18 x J What happens in a hydrogen lamp? Line Emission Spectrum of Hydrogen Atoms

25 E = h E = h

26 Hydrogen Atomic Spectra Line Emission Spectrum of Hydrogen Atoms

27 E photon =  E = E f - E i E f = -R H ( ) 1 n2n2 f E i = -R H ( ) 1 n2n2 i i f  E = R H ( ) 1 n2n2 1 n2n2 n f = 1 n i = 2 n f = 1 n i = 3 n f = 2 n i = 3 R H (constant) = 2.18 x J 1 = R n2n2 1 m2m2 1 - E = h x C/λ R = X nm -1 m = initial n = final

28 De Broglie (1924) reasoned that e - is both particle and wave. = h/mv v = velocity of e - m = mass of e - Why is e - energy quantized? h = 6.63 x Js

29 = h/mv = 6.63 x J.S ((Kg.m 2 /S 2 )/J) / ((2.5 x Kg) x (15.6 m/s)) = 1.7 x m = 1.7 x nm What is the de Broglie wavelength (in nm) associated with a 2.5 g Ping-Pong ball traveling at 15.6 m/s? m (mass) in kgh in J s V ( velocity) in (m/s), J = Kg.m 2 /S 2 )

30 Uncertainty Principle Problem of defining nature of electrons in atoms solved by W. Heisenberg. Cannot simultaneously define the position and momentum (= mv) of an electron. We define e- energy exactly but accept limitation that we do not know exact position. Problem of defining nature of electrons in atoms solved by W. Heisenberg. Cannot simultaneously define the position and momentum (= mv) of an electron. We define e- energy exactly but accept limitation that we do not know exact position. W. Heisenberg

31 Schrodinger Wave Equation In 1926 Schrodinger wrote an equation that described both the particle and wave nature of the e - Wave function (  psi) describes: psi 1. energy of e - with a given  2. probability of finding e - in a volume of space Schrodinger’s equation can only be solved exactly for the hydrogen atom. Must approximate its solution for multi-electron systems.

32 Existence (and energy) of electron in atom is described by its unique wave function . Pauli exclusion principle - no two electrons in an atom can have the same four quantum numbers. Schrodinger Wave Equation  = fn(n, l, m l, m s ) Each seat is uniquely identified (E, R12, S8) Each seat can hold only one individual at a time

33 Schrodinger Wave Equation  fn(n, l, m l, m s ) principal quantum number n n = 1, 2, 3, 4, …. n=1 n=2 n=3 distance of e - from the nucleus

34 Electron Radial Distribution01

35 Electron Radial Distribution02 s Orbital Shapes:

36 1s Orbital

37 2s Orbital

38 3s Orbital

39  = fn(n, l, m l, m s ) angular momentum quantum number l for a given value of n, l = 0, 1, 2, 3, … n-1 n = 1, l = 0 n = 2, l = 0 or 1 n = 3, l = 0, 1, or 2 Shape of the “volume” of space that the e - occupies l = 0 s orbital l = 1 p orbital l = 2 d orbital l = 3 f orbital Schrodinger Wave Equation

40 QUANTUM NUMBERS  = fn(n, l, m l, m s ) The shape, size, and energy of each orbital is a function of 3 quantum numbers: n (major) ---> shell l (angular) ---> subshell m l (magnetic) ---> designates an orbital within a subshell

41 SymbolValuesDescription n (major)1, 2, 3,..Orbital size and energy l (angular)0, 1, 2,.. n-1 Orbital shape and energy (subshell) m l (magnetic)-l..0..+lOrbital orientation # of orbitals in subshell = 2 l + 1 # of orbitals in subshell = 2 l + 1 QUANTUM NUMBERS

42  = fn(n, l, m l, m s ) angular momentum quantum number l for a given value of n, l = 0, 1, 2, 3, … n-1 n = 1, l = 0 n = 2, l = 0 or 1 n = 3, l = 0, 1, or 2 Shape of the “volume” of space that the e - occupies l = 0 s orbital l = 1 p orbital l = 2 d orbital l = 3 f orbital Schrodinger Wave Equation

43 l = 0 (s orbitals) l = 1 (p orbitals) 7.6

44 Electron Radial Distribution03 p Orbital Shapes:

45 l = 2 (d orbitals) 7.6

46  = fn(n, l, m l, m s ) magnetic quantum number m l for a given value of l m l = -l, …., 0, …. +l orientation of the orbital in space if l = 1 (p orbital), m l = -1, 0, or 1 if l = 2 (d orbital), m l = -2, -1, 0, 1, or 2 Schrodinger Wave Equation 7.6

47 m l = -1m l = 0m l = 1 m l = -2m l = -1m l = 0m l = 1m l = 2

48  = fn(n, l, m l, m s ) spin quantum number m s m s = +½ or -½ Schrodinger Wave Equation m s = -½m s = +½

49 Existence (and energy) of electron in atom is described by its unique wave function . Pauli exclusion principle - no two electrons in an atom can have the same four quantum numbers. Schrodinger Wave Equation  = fn(n, l, m l, m s ) Each seat is uniquely identified (E, R12, S8) Each seat can hold only one individual at a time

50  = fn(n, l, m l, m s ) angular momentum quantum number l for a given value of n, l = 0, 1, 2, 3, … n-1 n = 1, l = 0 n = 2, l = 0 or 1 n = 3, l = 0, 1, or 2 Shape of the “volume” of space that the e - occupies l = 0 s orbital l = 1 p orbital l = 2 d orbital l = 3 f orbitalf orbital Schrodinger Wave Equation 7.6

51 f-Orbitals

52 Schrodinger Wave Equation  = fn(n, l, m l, m s ) Shell – electrons with the same value of n Subshell – electrons with the same values of n and l Orbital – electrons with the same values of n, l, and m l How many electrons can an orbital hold? If n, l, and m l are fixed, then m s = ½ or - ½  = (n, l, m l, ½ ) or  = (n, l, m l, - ½ ) An orbital can hold 2 electrons

53 How many 2p orbitals are there in an atom? 2p n=2 l = 1 If l = 1, then m l = -1, 0, or +1 3 orbitals How many electrons can be placed in the 3d subshell? 3d n=3 l = 2 If l = 2, then m l = -2, -1, 0, +1, or +2 5 orbitals which can hold a total of 10 e -

54 Effective Nuclear Charge01 Electron shielding leads to energy differences among orbitals within a shell. Net nuclear charge felt by an electron is called the effective nuclear charge (Z eff ).

55 Effective Nuclear Charge02 Z eff is lower than actual nuclear charge. Z eff increases toward nucleus Energy of electron 1)The higher the main shell the more the energy of electron. 2)Subshell also contribute to the energy of electron: ns > np > nd > nf This explains certain periodic changes observed.

56 Effective Nuclear Charge03

57 Energy of orbitals in a multi-electron atom Energy depends on n and l n=1 l = 0 n=2 l = 0 n=2 l = 1 n=3 l = 0 n=3 l = 1 n=3 l = 2

58 “Fill up” electrons in lowest energy orbitals (Aufbau principle) H 1 electron H 1s 1 He 2 electrons He 1s 2 Li 3 electrons Li 1s 2 2s 1 Be 4 electrons Be 1s 2 2s 2 B 5 electrons B 1s 2 2s 2 2p 1 C 6 electrons ??

59 C 6 electrons The most stable arrangement of electrons in subshells is the one with the greatest number of parallel spins (Hund’s rule). C 1s 2 2s 2 2p 2 N 7 electrons N 1s 2 2s 2 2p 3 O 8 electrons O 1s 2 2s 2 2p 4 F 9 electrons F 1s 2 2s 2 2p 5 Ne 10 electrons Ne 1s 2 2s 2 2p 6

60 Order of orbitals (filling) in multi-electron atom 1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s < 4f< 5d< 6p< 7s< 5f< 6d< 7p

61 Electron Configuration of Atoms Rules of Aufbau Principle: 1.Lower energy orbitals fill first. 2.Each orbital holds two electrons; each with different m s. 3.Half-fill degenerate orbitals before pairing electrons.

62 What is the electron configuration of Mg? Mg 12 electrons 1s < 2s < 2p < 3s < 3p < 4s 1s 2 2s 2 2p 6 3s = 12 electrons Abbreviated as [Ne]3s 2 What are the possible quantum numbers for the last (outermost) electron in Cl? Cl 17 electrons1s < 2s < 2p < 3s < 3p < 4s 1s 2 2s 2 2p 6 3s 2 3p = 17 electrons Last electron added to 3p orbital n = 3l = 1m l = -1, 0, or +1m s = ½ or -½

63 ns 1 ns 2 ns 2 np 1 ns 2 np 2 ns 2 np 3 ns 2 np 4 ns 2 np 5 ns 2 np 6 d1d1 d5d5 d 10 4f 5f Electron Configuration and the Periodic Table

64 Electron Configuration of Atoms 06

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66 a)S [Ne]3s 2 3p 4 Using periodic table write Noble gas notation for the following elements: b)Fe [Ar] 4s 2 3d 6 c)Se [Ar] 4s 2 3d 10 4p 4 d)Gd [Xe]6s 2 4f 7 5d1 1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s < 4f< 5d< 6p< 7s< 5f< 6d< 7p

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68 Electron Configuration of Atoms 08 Anomalous Electron Configurations: Result from unusual stability of half-filled & full-filled subshells. Chromium should be [Ar] 4s 2 3d 4, but is [Ar] 4s 1 3d 5 Copper should be [Ar] 4s 2 3d 9, but is [Ar] 4s 1 3d 10

69 Electron Spin Quantum Number Electron Spin Quantum Number Diamagnetic Diamagnetic : NOT attracted to a magnetic field Diamagnetic Paramagnetic : substance is attracted to a magnetic field. Substance has unpaired electrons. Diamagnetic Diamagnetic : NOT attracted to a magnetic field Diamagnetic Paramagnetic : substance is attracted to a magnetic field. Substance has unpaired electrons. * See page 261 of your book for molecular structure of N2 vs O2

Molecular Orbital Theory: Other Diatomic Molecules

71 Paramagnetic unpaired electrons 2p Diamagnetic all electrons paired 2p

72 Periodic Properties01

73 Effective nuclear charge (Z eff ) is the “positive charge” felt by an electron. Na Mg Al Si ~ Z eff Core Z Radius/pm Z eff = Z -  0 <  < Z (  = shielding constant) Z eff  Z – number of inner or core electrons Within a Period as Z eff increases radius decreases (Sigma)

74 Size of the atoms

75 (pm)