Quantum Theory and the. Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

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1 Quantum Theory and the Electronic Structure of Atoms Chapter 7 Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

2 Properties of Waves Wavelength (λ) is the distance between identical points on successive waves. Amplitude is the vertical distance from the midline of a wave to the peak or trough. 7.1

3 Properties of Waves Frequency (ν) is the number of waves that pass through a particular point in 1 second (Hz = 1 cycle/s). The speed (u) of the wave = λ x ν 7.1

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

5 7.1

6 A photon has a frequency of 6.0 x 10 4 Hz. Convert this frequency into wavelength (nm). Does this frequency fall in the visible region? λ x ν = c λ = c/ν λ = 3.00 x 10 8 m/s / 6.0 x 10 4 Hz λ = 5.0 x 10 3 m λ = 5.0 x nm λ ν Radio wave 7.1

7 Mystery #1, Black Body Problem Solved by Planck in 1900 Energy (light) is emitted or absorbed in discrete units (quantum). E = h x ν Planck s constant (h) h = 6.63 x J s 7.1

8 Mystery #2, Photoelectric Effect Solved by Einstein in 1905 hν Light has both: 1. wave nature 2. particle nature KE e - Photon is a particle of light hν = KE + BE KE = hν -BE 7.2

9 When copper is bombarded with high-energy electrons, X rays are emitted. ed Calculate a the energy e (in joules) associated with the photons if the wavelength of the X rays is nm. E = h x ν E = h x c / λ E = 6.63 x (J s) x 3.00 x 10 8 (m/s) / x 10-9 (m) E = 1.29 x J 7.2

10 Line Emission Spectrum of Hydrogen Atoms 7.3

11 7.3

12 Bohr s Model of the Atom (1913) 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 1 n E n = -R H ( ) n 2 n (principal quantum number) = 1,2,3, R H (Rydberg constant) = 2.18 x J 7.3

13 E = hν E = hν 7.3

14 n i = 3 n i = 3 n i = 2 n f = 2 E photon = ΔE = E f -E i 1 E f = -R H ( ) n 2 f 1 E i = -R H ( ) n 2 i 1 1 n 2 ΔE E = R H ( ) i n 2 f n f = 1 n f = 1 7.3

15 Calculate the wavelength (in nm) of a photon emitted by a hydrogen atom when its electron drops from the n = 5 state to the n = 3 state. E photon = 1 1 n 2 ΔE = R H ( ) i n 2 f E photon = 2.18 x J x (1/25-1/9) E photon = ΔE = x J photon E photon = h x c / λ λ = h x c / E photon λ = 6.63 x (J s) x 3.00 x 10 8 (m/s)/1.55 x J λ = 1280 nm 7.3

16 Why is e - energy quantized? De Broglie (1924) reasoned that e - is both particle and wave. 2πr = nλ u = velocity of e- m = mass of e- λ = h mu 7.4

17 What is the de Broglie wavelength (in nm) associated with a 2.5 gping-pong Pong ball traveling at 15.6 m/s? λ = h/mu h in J s m in kg u in (m/s) λ = 6.63 x / (2.5 x 10-3 x 15.6) λ = 1.7 x m = 1.7 x nm 7.4

18 Chemistry in Action: Laser The Splendid Light Laser light is (1) intense, (2) monoenergetic, and (3) coherent

19 Chemistry in Action: Electron Microscopy λ e = nm STM image of iron atoms on copper surface

20 Schrodinger Wave Equation In 1926 Sh Schrodinger wrote an equation that described both the particle and wave nature of the e - Wave function (Ψ) describes: 1. energy e of e - with a given Ψ 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. 7.5

21 Schrodinger Wave Equation Ψ = fn(n, l, m l, m s ) principal quantum number n n = 1, 2, 3, 4,. distance of e - from the nucleus n=1 n=2 n=3 7.6

22 Where 90% of the e - density is found for the 1s orbital 7.6

23 Schrodinger Wave Equation Ψ = 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 1, l = 0 n = 2, l = 0 or 1 n = 3, l = 0, 1, or 2 l = 0 s orbital l = 1 p orbital l = 2 d orbital l = 3 f orbital Shape of the volume of space that the e - occupies 7.6

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

25 l = 2 (d orbitals) 7.6

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

27 m l = -1 m l = 0 m l = 1 l l l m l = -2 m l = -1 m l = 0 m l = 1 m l = 2 7.6

28 Schrodinger Wave Equation Ψ = fn(n, l, m l, m s ) spin quantum number m s m s = +½ or -½ m s = +½ m s =-½ 7.6

29 Schrodinger Wave Equation Ψ = fn(n, l, m l, m s ) Existence (and energy) of electron in atom is described by its unique wave function Ψ. Pauli exclusion principle - no two electrons in an atom can have the same four quantum numbers. Each seat is uniquely identified (E, R12, S8) Each seat can hold only one individual at a time 7.6

30 7.6

31 Schrodinger Wave Equation Ψ = 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 Ψ = (n, l, m l, ½) or Ψ = (n, l, m l, -½) An orbital can hold 2 electrons 7.6

32 How many 2p orbitals are there in an atom? n=2 2p l = 1 If l = 1, then m l = -1, 0, or +1 3 orbitals How many electrons can be placed in the 3d subshell? n=3 If l = 2, then m l = -2, -1, 0, +1, or +2 3d 5 orbitals which can hold a total of 10 e - l = 2 7.6

33 Energy of orbitals in a single electron atom Energy only depends on principal quantum number n n=3 n=2 1 E n = -R H ( ) n 2 n=1 7.7

34 Energy of orbitals in a multi-electron atom Energy depends on n and l n=3 l = 2 n=3 l = 0 n=2 l = 0 n=3 l = 1 n=2 l = 1 n=1 l = 0 7.7

35 Fill up electrons in lowest energy orbitals (Aufbau principle)?? Li Be B C electrons B Be Li 1s 1s 2 2s 2 2s 2 2p 12 1 H 1 electron He 2 electrons He H 1s

36 The most stable arrangement of electrons in subshells is the one with the greatest t number of parallel spins (Hund s rule). C O F Ne electrons Ne C N O F 1s 2 2 2s 2 2 2p

37 Order of orbitals (filling) in multi-electron atom 1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s 7.7

38 Electron configuration is how the electrons are distributed among the various atomic orbitals in an atom. principal quantum number n 1s 1 number of electrons in the orbital or subshell angular momentum quantum number l Orbital diagram H 1s 1 7.8

39 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 [Ne] 1s 2 2s 2 2p 6 What are the possible quantum numbers for the last (outermost) electron in Cl? Cl 17 electrons 1s 2 2s 2 2p 6 3s 2 3p 5 1s < 2s < 2p < 3s < 3p < 4s Last electron added to 3p orbital = 17 electrons n = 3 l = 1 m l = -1, 0, or +1 m s = ½ or -½ 7.8

40 Outermost subshell being filled with electrons 7.8

41 7.8

42 Paramagnetic unpaired electrons Diamagnetic all electrons paired 2p 2p 7.8

43 Chemistry Mystery: Discovery of Helium In 1868, Pierre Janssen detected a new dark line in the solar emission spectrum that did not match known emission lines Mystery element was named Helium In 1895, William Ramsey discovered helium in a mineral of uranium (from alpha decay).