1 Quantum Theory and the Electronic Structure of AtomsChapter Seven Quantum Theory and the Electronic Structure of Atoms

2 Wave: a vibrating disturbance by which energy is transmitted. Chapter Seven / Quantum Theory and the Electronic Structure of Atoms From Classical Physics to Quantum Theory We have to understand something about the nature of wave before talking about Quantum theory. Wave: a vibrating disturbance by which energy is transmitted. Wavelength (λ) lambda: is the distance between identical points on successive waves. Frequency (ν) nu: is the number of waves that pass through a particular point in 1 second. Amplitude : is the vertical distance from the midline of a wave to the peak.

3 Frequency is measured in hertz (Hz) 1 Hz = 1 cycle/s Chapter Seven / Quantum Theory and the Electronic Structure of Atoms From Classical Physics to Quantum Theory Wave speed (u): depend on type of wave and the nature of the medium through which the wave is traveling. Wavelength usually expressed in units of meter, centimeter, or nanometer. Frequency is measured in hertz (Hz) 1 Hz = 1 cycle/s Normally the word cycle is left out and we say and we expressed frequency as for example 25/s u= λν

4 The speed of light is known as 3 x 108 m/s Chapter Seven / Quantum Theory and the Electronic Structure of Atoms From Classical Physics to Quantum Theory Example: The wavelength of the green light from a traffic signal is centered at 522 nm. What is the frequency of this radiation? u =λν ν=u/λ The speed of light is known as 3 x 108 m/s Because the speed of light is in m we have to change the wavelength to m λ = 522 x 10-9 m ν = 3 x 108 / 522 x 10-9 = 5.75 x 1014 Hz.

5 for all electromagnetic radiation c = λν Chapter Seven / Quantum Theory and the Electronic Structure of Atoms From Classical Physics to Quantum Theory There are many type of waves, such as water waves, sound waves and light waves. Clerk Maxwell proposed in 1973 that visible light consists of electromagnetic wave has an electric field component and a magnetic filed component. The two components have the same wavelength and frequency, and hence the speed. Electromagnetic radiation is the emission and transmission of energy in the form of electromagnetic waves. for all electromagnetic radiation c = λν Where c is the speed of light = 3 x 108 m/s

6 From Classical Physics to Quantum TheoryChapter Seven / Quantum Theory and the Electronic Structure of Atoms From Classical Physics to Quantum Theory

7 Chapter Seven / Quantum Theory and the Electronic Structure of AtomsFrom Classical Physics to Quantum Theory Example: A photon has a frequency of 6.0 x 104 Hz. Convert this frequency into wavelength (nm)? c = λν λ = c/ν = 3 x108 / 6 x104 =5 x 103 m = 5 x 1012 nm

8 The energy of a signal quantum (E):Chapter Seven / Quantum Theory and the Electronic Structure of Atoms Planck’s Quantum Theory When solid are heated they emit electromagnetic radiation over a wide range of wavelength. Example is the dull red glow of an electric heater and the bright white light of tungsten light bulb. the amount of radiant energy emitted by an object at a certain temperature depends on the wavelength according to Plank the atoms and molecules could emit (or adsorb) energy only in discrete quantities (quantum). Quantum is the smallest quantity of energy that can be emitted (or absorbed) in the form of electromagnetic radiation. The energy of a signal quantum (E): Where h is planck’s constant

9 Chapter Seven / Quantum Theory and the Electronic Structure of AtomsPlanck’s Quantum Theory According to the quantum theory energy is always emitted in integral multiples of hν, for example hν, 2hν, 3hν, …… but never for exmaple 1.67hν. Example: Calculate the energy (in J) of: (a) a photon with a wavelength of 5.00 x 104 nm (IR region) (b) a photon with a wavelength of 5.00 x 10-2 nm (X-ray region) a- λ= 5 x 104nm = 5 x 104 x 10-9 = 5 x 10-5m b- λ= 5 x 10-2 nm = 5 x 10-2 x 10-9 = 5 x 10-11m

10 Chapter Seven / Quantum Theory and the Electronic Structure of AtomsBohr’s Theory of the Hydrogen Atom Bohr’s greatest contribution to science was in building a simple model of the atom. It was based on understanding the SHARP LINE SPECTRA of excited atoms. Niels Bohr ( ) (Nobel Prize, 1922)

11 Chapter Seven / Quantum Theory and the Electronic Structure of AtomsBohr’s Theory of the Hydrogen Atom Emission spectra is either continuous or line spectra of radiation emitted by substances. Continuous is a common feature to the emission spectra of the sun and of a heated solid; that is, all wavelengths of visible light are represented in the spectra.

12 Bohr’s Theory of the Hydrogen AtomChapter Seven / Quantum Theory and the Electronic Structure of Atoms Bohr’s Theory of the Hydrogen Atom

13 Line spectra is the light emission only at specific wavelengths. Chapter Seven / Quantum Theory and the Electronic Structure of Atoms Bohr’s Theory of the Hydrogen Atom Emission spectra is either continuous or line spectra of radiation emitted by substances. Continuous is a common feature to the emission spectra of the sun and of a heated solid; that is, all wavelengths of visible light are represented in the spectra. The emission spectra of atoms in the gas phase do not show a continuous spread of wavelengths from red to violet; rather, the atoms produce bright lines in different parts of the visible spectrum. Line spectra is the light emission only at specific wavelengths. Excited atoms emit light of only certain wavelengths The wavelengths of emitted light depend on the element.

14 Chapter Seven / Quantum Theory and the Electronic Structure of AtomsBohr’s Theory of the Hydrogen Atom Emission spectrum of any atom is a finger print (lines appeared at specific wavelengths) H Hg Stopped here Ne

15 Chapter Seven / Quantum Theory and the Electronic Structure of AtomsBohr’s Theory of the Hydrogen Atom Bohr postulated that the electron is allowed to occupy only certain orbits of specific energies and the energies of the electron are quantized. According to Bohr the emission spectrum of the H atom results from the following: the hydrogen atom is energised then electron excited to higher energy orbit and then drop to a lower-energy orbit and emitting a quantum of energy ( a photon) in the form of light.

16 Chapter Seven / Quantum Theory and the Electronic Structure of AtomsBohr’s Theory of the Hydrogen Atom The equation that represent the energies that an electron in hydrogen atom can occupy are given by: RH is the Rodberg constant (2.18 x J), n is an integer called the principle quantum number (n= 1,2,3,…..). when n =1 this is refer to as ground state or the ground level. Which refer to the lowest energy state of a system. n=2,3,4…. Is called an excited state or excited level, which is higher in energy than the ground state.

17 Chapter Seven / Quantum Theory and the Electronic Structure of AtomsBohr’s Theory of the Hydrogen Atom The journey from a lower step to a higher step is an energy-requiring process. Whereas movement from a higher step to a lower step is an energy releasing process.

18 If nf > ni → (+ve) → ΔE (+ve) → Energy is absorbed Chapter Seven / Quantum Theory and the Electronic Structure of Atoms Bohr’s Theory of the Hydrogen Atom If nf > ni → (+ve) → ΔE (+ve) → Energy is absorbed If ni > nf → (-ve) → ΔE (-ve) → Energy is emitted

19 Bohr’s Theory of the Hydrogen AtomChapter Seven / Quantum Theory and the Electronic Structure of Atoms Bohr’s Theory of the Hydrogen Atom

20 Chapter Seven / Quantum Theory and the Electronic Structure of AtomsBohr’s Theory of the Hydrogen Atom Example: What is the wavelength of a photon (in nm) emitted during a transition from the ni = 5 state to the nf = 2 state in the hydrogen atom? ni=5, nf = 2 , λ=?

21 De Broglie deduced that the particle and wave Chapter Seven / Quantum Theory and the Electronic Structure of Atoms The Dual Nature of the Electron De Broglie suggested that particles such as electron can posses wave properties. According to de Borglie, an electron bond to nucleus behave like a standing wave. De Broglie deduced that the particle and wave prosperities are related by the expression Where λ wavelenght of moving particle, m mass (kg), u velocity of moving particle.

22 Chapter Seven / Quantum Theory and the Electronic Structure of AtomsThe Dual Nature of the Electron Example What is the de Broglie wavelength (in nm) associated with a 2.5 g Ping-Pong ball traveling at 15.6 m/s? λ = ?, m= 2.5g = 2.5x10-3kg, u=15.6m/s λ=1.7x10-31m = 1.7x10-22nm.

23 Chapter Seven / Quantum Theory and the Electronic Structure of AtomsQuantum numbers Bohr theory did not provide a complete description of electronic behaviour in atoms and it location around the nucleus. In 1926 Erwin Schrödinger wrote an equation that specifies the energy states of the electron in a hydrogen atom and identifies the corresponding wave functions Ψ. These energy states and wave functions are characterized by a set of Quantum Numbers . Quantum numbers may be viewed as an electrons address. Schrödinger’s equation can only be solved exactly for the hydrogen atom. Must approximate its solution for multi-electron systems. Quantum number are a set of four values that define the energy state of an electron in an atom.

24 Chapter Seven / Quantum Theory and the Electronic Structure of AtomsQuantum numbers 1-The Principle Quantum Number (n): n has integer value (1,2,3,…). n determine the energy of an orbital. Its also related to the distance between the electron and the nucleus. The larger n the grater the distance. n=1 n=2 n=3

25 Chapter Seven / Quantum Theory and the Electronic Structure of AtomsQuantum numbers 2- The Angular Momentum Quantum Number (l) The value of l depend on the value of n, l= 0, (n-1). If n=1 then l =1-1 = 0 If n =2 then l = 0 , (2-1) = 0 , 1 If n =3 then I = 0, 1 , (3-1) = 0 , 1 , 2 And so on. l determine the shape of the orbitals. The value of l is generally designated by the letters s, p, d, …..as follows: l 1 2 3 4 Name of orbital s p d f g

26 Chapter Seven / Quantum Theory and the Electronic Structure of AtomsQuantum numbers 3- The Magnetic Number (ml) The value of ml depend on the value of l. ml = -l ,…….0,……+l If l=0 then ml =0 If l =1 then ml = -1,0,1 If l =2 then ml = -2,-1,0,1,2 And so on. ml describe the orientation of the orbital in space.

27 Chapter Seven / Quantum Theory and the Electronic Structure of AtomsQuantum numbers 4- The Electron Spin Quantum Number (ms) ms has two value – ½ or + ½ . ms determine the spin of electron.

28 Chapter Seven / Quantum Theory and the Electronic Structure of AtomsQuantum numbers Example : List the values of n, l and ml for orbitals in 4d subshell? What is the total number of orbital in 4d? n= 4 for d l=2 ml = -2,-1,0,1,2 Number of orbital = 5

29 Chapter Seven / Quantum Theory and the Electronic Structure of AtomsAtomic Orbitals 2l +1

30 Chapter Seven / Quantum Theory and the Electronic Structure of AtomsAtomic Orbitals Example What is the total number of orbitals associated with the principal quantum number n = 3 ? n=3 l=0,1,2 1- ml = 0 ======> 1 orbital 2- ml = -1,0,1 =====> 3 orbital 2- ml= -2,-1,0,1,2 ======> 5 orbital Total number of orbital 9 Or (2x0 +1) + (2x1 +1) + (2x2 +1) = = 9 OR Number of orbital = n2 = 32 = 9

31 Chapter Seven / Quantum Theory and the Electronic Structure of AtomsAtomic Orbitals The four quantum number for specific electron can written as (n,l,ml,ms). Example : Write the four quantum numbers for an electron in a 3p orbital? n=3 , l = 1, ml= -1,0,1 , ms= - ½ or ½ (3,1,-1,-1/2) (3,1,0,-1/2) (3,1,1,-1/2) (3,1,-1,1/2) (3,1,0,1/2) (3,1,1,1/2)

32 Chapter Seven / Quantum Theory and the Electronic Structure of AtomsAtomic Orbitals S orbital l=0 Spherical

33 Chapter Seven / Quantum Theory and the Electronic Structure of AtomsAtomic Orbitals P orbital l=1 dumbbell ml = -1 ml = 0 ml = 1

34 Chapter Seven / Quantum Theory and the Electronic Structure of AtomsAtomic Orbitals d orbital l=2 ml = -2 ml = -1 ml = 0 ml = 1 ml = 2

35 1s < 2s=2p < 3s=3p=3d < 4s=4p=4d=4f <…….. Chapter Seven / Quantum Theory and the Electronic Structure of Atoms The Energies of Orbitals For hydrogen atom, the energies of hydrogen orbitals increase as following: 1s < 2s=2p < 3s=3p=3d < 4s=4p=4d=4f <…….. Energy only depends on principal quantum number n Orbitals on the same energy level have the same energy. For atom with multi electron, energy of orbitals depend on n and l. it follow: 1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s

36 The Energies of OrbitalsChapter Seven / Quantum Theory and the Electronic Structure of Atoms The Energies of Orbitals For hydrogen atom

37 The Energies of OrbitalsChapter Seven / Quantum Theory and the Electronic Structure of Atoms The Energies of Orbitals For multi electron atom

38 The Energies of OrbitalsChapter Seven / Quantum Theory and the Electronic Structure of Atoms The Energies of Orbitals Order of orbitals (filling) in multi-electron atom 1 2 3 1s 4 5 2s 2p 6 s sublevel 2 electrons p sublevel 6 electrons d sublevel electrons f sublevel electrons 3s 3p 3d 7 4s 4p 4d 4f 8 5s 5p 5d 5f 6s 6p 6d Stop here 7s 7p 1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s < 4f < 5d < 6p < 7s < 5f < 6d < 7p

39 1s1 number of electrons in the orbital or subshell principal quantumChapter Seven / Quantum Theory and the Electronic Structure of Atoms Electron configuration Electron configuration: is how the electrons are distributed among the various atomic orbitals in an atom. number of electrons in the orbital or subshell 1s1 principal quantum number n angular momentum quantum number l

40 Chapter Seven / Quantum Theory and the Electronic Structure of AtomsThe Pauli Exclusion principle NO two electrons in an atom can have the same set of four quantum numbers Stopped here ? ? He 2 electrons He 1s2

41 Chapter Seven / Quantum Theory and the Electronic Structure of AtomsAufbau principle The electrons are added one by one to the atomic orbitals Li 3 electrons Li 1s22s1

42 Chapter Seven / Quantum Theory and the Electronic Structure of AtomsAufbau principle The electrons are added one by one to the atomic orbitals Be 4 electrons Be 1s22s2

43 Chapter Seven / Quantum Theory and the Electronic Structure of AtomsAufbau principle The electrons are added one by one to the atomic orbitals B 5 electrons B 1s22s22p1

44 ? ? C 6 electrons C 1s22s22p2 Hund’s RuleChapter Seven / Quantum Theory and the Electronic Structure of Atoms Hund’s Rule The most stable arrangement of electrons in subshells is the one with the greatest number of parallel spins ? ? C 6 electrons C 1s22s22p2

45 N 7 electrons N 1s22s22p3 Hund’s RuleChapter Seven / Quantum Theory and the Electronic Structure of Atoms Hund’s Rule The most stable arrangement of electrons in subshells is the one with the greatest number of parallel spins N 7 electrons N 1s22s22p3

46 Chapter Seven / Quantum Theory and the Electronic Structure of AtomsAufbau principle The electrons are added one by one to the atomic orbitals O 8 electrons O 1s22s22p4

47 Chapter Seven / Quantum Theory and the Electronic Structure of AtomsAufbau principle The electrons are added one by one to the atomic orbitals F 9 electrons F 1s22s22p5

48 Chapter Seven / Quantum Theory and the Electronic Structure of AtomsAufbau principle The electrons are added one by one to the atomic orbitals Ne 10 electrons Ne 1s22s22p6

49 Chapter Seven / Quantum Theory and the Electronic Structure of AtomsOrbital diagram The electron configuration can also represented by the orbital diagram In the Orbital Diagram: Each box represents one orbital. Half-arrows represent the electrons. The direction of the arrow represents the spin of the electron.

50 Chapter Seven / Quantum Theory and the Electronic Structure of AtomsOrbital diagram 1 2 3 1s 4 Example: What is the electron configuration of Mg? Mg atom has 12 electrons (from Periodic table (atomic number)) The Electron Configuration: 1s22s22p63s2 = 12 electrons Orbital Diagram: 1s s p s2 5 2s 2p 6 3s 3p 3d 7 4s 4p 4d 4f 8 5s 5p 5d 5f 6s 6p 6d 7s 7p

51 Chapter Seven / Quantum Theory and the Electronic Structure of AtomsOrbital diagram 1 2 3 1s 4 What is the electron configuration of K? K atom has 19 electrons (from Periodic table (atomic number)) The Electron Configuration: 1s22s22p63s2 3p6 4s1 = 19 electrons Orbital Diagram: 1s s p s p s1 5 2s 2p 6 3s 3p 3d 7 4s 4p 4d 4f 8 5s 5p 5d 5f 6s 6p 6d 7s 7p

52 Chapter Seven / Quantum Theory and the Electronic Structure of AtomsOrbital diagram 1 2 3 1s 4 What is the electron configuration of K+1? Atomic number19 Electron 19 -1= 18 K atom has 18 electrons (from Periodic table (atomic number)) The Electron Configuration: 1s22s22p63s2 3p6 = 18 electrons Orbital Diagram: 1s s p s p6 5 2s 2p 6 3s 3p 3d 7 4s 4p 4d 4f 8 5s 5p 5d 5f 6s 6p 6d 7s 7p

53 Chapter Seven / Quantum Theory and the Electronic Structure of AtomsShort Notation Short Notation (abbreviation): To write the electron configuration of an element in short notation, write the symbol of the Noble gas element in the previous period in brackets followed by the symbol of highest filled subshells in the outermost shells.

54 Chapter Seven / Quantum Theory and the Electronic Structure of AtomsAtomic Orbitals Example For Cl atom answer the following questions: a) Write the electron configuration? b) Draw the orbital diagram? c) Write the electron configuration in short notation? d) What are the possible quantum numbers for the last (outermost) electron in Cl? Answer: a) Cl atom has 17 electrons (from Periodic table (atomic number)) The Electron Configuration: 1s2 2s2 2p6 3s2 3p5 = 17 electrons

55 Chapter Seven / Quantum Theory and the Electronic Structure of AtomsAtomic Orbitals b) Draw the orbital diagram? Orbital Diagram: 1s s p s p5 c) Short notation: [Ne] 3s2 3p5 d) n= 3 l= 1 ml= 0 ms= - ½

56 Chapter Seven / Quantum Theory and the Electronic Structure of AtomsAtomic Orbitals Example What is The electron configuration of 11Na ,12Mg ,16S ? 11Na 1s2 2s2 2p6 3s (OR) [Ne] 3s1 12Mg 1s2 2s2 2p6 3s (OR) [Ne] 3s2 16S 1s2 2s2 2p6 3s2 3p (OR) [Ne] 3s2 3p4 Stopped here

57 The Building-Up PrincipalChapter Seven / Quantum Theory and the Electronic Structure of Atoms The Building-Up Principal Outermost subshell being filled with electrons

58 Development of the Periodic TableChapter Eight/ Periodic Relationships Among the Elements Development of the Periodic Table

59 Chapter Seven / Quantum Theory and the Electronic Structure of AtomsAtomic Orbitals Noble Gases: elements with electron configuration of complete s & p subshell (He, Ne, Ar, Kr, Xe, Rn), Group 8A

60 Chapter Seven / Quantum Theory and the Electronic Structure of AtomsAtomic Orbitals Representative Elements: elements with electron configuration of incompletely filled s or p subshell. Elements in Groups 1A-to-7A

61 Chapter Seven / Quantum Theory and the Electronic Structure of AtomsAtomic Orbitals Transition Elements: elements with electron configuration of incompletely filled d subshells or readily give rise to cations that have incompletely filled d subshells. Elements in Groups 1B-to-7B

62 Chapter Seven / Quantum Theory and the Electronic Structure of AtomsExceptions The Stability of Half Filled & Filled d Orbitals 29Cu:1s2 2s2 2p6 3s2 3p6 4s2 3d9 [Ar] 4s2 3d9 The stability of Filled d orbital → 29Cu: [Ar] 4s1 3d10

63 Chapter Seven / Quantum Theory and the Electronic Structure of AtomsAtomic Orbitals 29Cu: [Ar] 4s13d10 47Ag:[Kr] 5s1 4d10 42Mo: [Kr] 5s1 4d5 24Cr: [Ar] 4s1 3d5

64 Chapter Seven / Quantum Theory and the Electronic Structure of AtomsAtomic Orbitals Paramagnetic substance: is the element that contain net unpaired electrons in the outermost subshell and is attracted by a magnet. e.g. Diamagnetic substance: is the element that do not contain net unpaired electrons (all electrons are paired) in the outermost subshell and is repelled by a magnet. Paramagnetic unpaired electrons 2p Diamagnetic all electrons paired 2p

65 Electronic configuration: 1s2 2s2 2p6 3s2 3p6 4s1 Chapter Seven / Quantum Theory and the Electronic Structure of Atoms Atomic Orbitals 19K Electronic configuration: 1s2 2s2 2p6 3s2 3p6 4s1 Short notation: [Ar] 4s1 Orbital diagram: Example 3s p s1 Net one unpaired electron → Paramagnetic substance

66 Electronic configuration: 1s2 2s2 2p6 Orbital diagram:Chapter Seven / Quantum Theory and the Electronic Structure of Atoms Atomic Orbitals Example 10Ne Electronic configuration: 1s2 2s2 2p6 Orbital diagram: 1s s p6 All electrons are paired → Diamagnetic substance

67 Chapter Seven / Quantum Theory and the Electronic Structure of AtomsAtomic Orbitals D P D P P P P P

68 What are the valence electrons of vanadium (V)? 23V: [Ar] 4s2 3d3Chapter Seven / Quantum Theory and the Electronic Structure of Atoms Atomic Orbitals Example What are the valence electrons of vanadium (V)? 23V: [Ar] 4s2 3d3 What are the valence electrons of Gallium (Ga)? 31Ga: [Ar] 4s2 3d10 4p1 The valence electrons are 4s2 4p1

69 Within a Period number of electrons increase Chapter Seven / Quantum Theory and the Electronic Structure of Atoms ns2np6 Periodic Classification of the Elements ns1 ns2np1 ns2np2 ns2np3 ns2np4 ns2np5 ns2 Within a Period number of electrons increase Within a group (n) increase d10 d1 d5 4f 5f

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