1 CHAPTER 6 The Structure of Atoms

2 Electromagnetic Radiation Mathematical theory that describes all forms of radiation as oscillating (wave- like) electric and magnetic fields Figure 7.1

3 Wave Properties Wavelength ( ): distance between consecutive crests or troughs Frequency ( ): number of waves that pass a given point in some unit of time (1 sec) -units of frequency 1/time such as 1/s = s -1 = Hz Amplitude (A): the maximum height of a wave Nodes: points of zero amplitude -every /2 wavelength Amplitude Node ( /2)

4 Wave Properties c =  for electromagnetic radiation Speed of light (c): x 10 8 m/s Example: What is the frequency of green light of wavelength 5200 Å ?

5 Electromagnetic Spectrum wavelength increases energy increases frequency increases?

6 E = h h = Planck’s constant = x Js Any object can gain or lose energy by absorbing or emitting radiant energy -only certain vibrations ( ) are possible (Quanta) -Energy of radiation is proportional to frequency ( ) Maxwell Planck Planck’s Equation

7 Light with a short (large ) has a large E Light with large (small ) has a small E E = h =hc/ Planck’s Equation Maxwell Planck

8 Planck’s Equation What is the energy of a photon of green light with wavelength 5200 Å ?  What is the energy of 1.00 mol of these photons?

9 Einstein and the Photon Photoelectric effect: the production of electrons (e - ) when light (photons) strikes the surface of a metal -introduces the idea that light has particle-like properties -photons: packets of massless “particles” of energy -energy of each photon is proportional to the frequency of the radiation (Planck’s equation)

10 Atomic Spectra and the Bohr Atom Line emission spectrum: electric current passing through a gas (usually an element) causing the atoms to be excited -This is done in a vacuum tube (at very low pressure) causing the gas to emit light

11 Atomic Spectra and the Bohr Atom Every element has a unique spectrum –-Thus we can use spectra to identify elements. –-This can be done in the lab, with stars, in fireworks, etc. H Hg Ne

12 Adsorption/Emission Spectra

13 Atomic Spectra Balmer equation (Rydberg equation): relates the wavelengths of the lines (colors) in the atomic spectrum finalint Principle quantum number

14 Atomic Spectra What is the wavelength of light emitted when the hydrogen atom’s energy changes from n = 4 to n = 2? n final = 2 n initial = 4

15 Bohr’s greatest contribution to science was in building a simple model of the atom It was based on an understanding of the SHARP LINE EMISSION SPECTRA of excited atoms Niels Bohr ( ) The Bohr Model

16 Any orbit should be possible and so is any energy  But a charged particle moving in an electric field should emit (lose) energy  End result is all matter should self-destruct Early view of atomic structure from the beginning of the 20th century -electron (e - ) traveled around the nucleus in an orbit The Bohr Model

17 The Bohr Atom In 1913 Neils Bohr incorporated Planck’s quantum theory into the hydrogen spectrum explanation –Here are the postulates of Bohr’s theory: 1. Atom has a definite and discrete number of energy levels (orbits) in which an electron may exist n – the principal quantum number As the orbital radius increases so does the energy (n-level) 1<2<3<4<5...

18 The Bohr Atom 2. An electron may move from one discrete energy level (orbit) to another, but to do so energy is emitted or absorbed 3. An electron moves in a spherical orbit around the nucleus -If e - are in quantized energy states, then ∆E of states can have only certain values -This explains sharp line spectra (distinct colors)

19 Bohr’s theory was a great accomplishment Received Nobel Prize, 1922  Problem with this theory- it only worked for H -introduced quantum idea artificially  -new theory had to developed Niels Bohr ( ) Atomic Spectra and Niels Bohr

20 de Broglie (1924) proposed that all moving objects have wave properties For light: E = mc 2 E = h = hc/ Therefore, mc = h/ For particles: (mass)(velocity) = h/ de Broglie (1924) proposed that all moving objects have wave properties For light: E = mc 2 E = h = hc/ Therefore, mc = h/ For particles: (mass)(velocity) = h/ Louis de Broglie ( ) Wave Properties of the Electron

21 The Wave Properties of the Electron In 1925 Louis de Broglie published his Ph.D. dissertation Electrons have both particle and wave-like characteristics All matter behave as both a particle and a wave –This wave-particle duality is a fundamental property of submicroscopic particles de Broglie’s Principle:

22 The Wave Nature of the Electron Determine the wavelength, in meters, of an electron, with mass 9.11 x kg, having a velocity of 5.65 x 10 7 m/s Remember Planck’s constant is x J s which is also equal to x kg m 2 /s, because 1 J = 1 kg m 2 /s 2

23 Erwin Schrödinger r (pm) pm. 50 pm 22 Schrödinger applied ideas of e - behaving as a wave to the problem of electrons in atoms -He developed the WAVE EQUATION -The solution gives a math expressions called WAVE FUNCTIONS,  -Each  describes an allowed energy state for an e - and gives the probability (  2 ) of the location for the e - Quantization is introduced naturally Quantum (Wave) Mechanics

24 The problem with defining the nature of electrons in atoms was solved by W. Heisenberg The problem with defining the nature of electrons in atoms was solved by W. Heisenberg  the position and momentum (momentum = mv) cannot be define simultaneously for an electron  ??? we can only define e - energy exactly but we cannot know the exact position of the e - to any degree of certainty. Or vice versa  ??? we can only define e - energy exactly but we cannot know the exact position of the e - to any degree of certainty. Or vice versa The problem with defining the nature of electrons in atoms was solved by W. Heisenberg The problem with defining the nature of electrons in atoms was solved by W. Heisenberg  the position and momentum (momentum = mv) cannot be define simultaneously for an electron  ??? we can only define e - energy exactly but we cannot know the exact position of the e - to any degree of certainty. Or vice versa  ??? we can only define e - energy exactly but we cannot know the exact position of the e - to any degree of certainty. Or vice versa Werner Heisenberg n-levels Uncertainty Principle

25 Schrödinger’s Atomic Model Atomic orbitals: regions of space where the probability of finding an electron around an atom is greatest quantum numbers: letter/number address describing an electrons location (4 total)

26 The Principal Quantum Number (n) n = 1, 2, 3, 4,... - electron’s energy depends mainly on n - n determines the size of the orbit the e - is in - each electron in an atom is assigned an n value - atoms with more than one e - can have more than one electron with the same n value (level) - each of these e- are in the same electron energy level (or electron shell) 8

27 Angular Momentum ( l ) l = 0, 1, 2, 3, 4, 5, (n-1) l = s, p, d, f, g, h, (n-1) -the names and shapes of the corresponding subshells (or suborbitals) in the orbital/energy level (n-level) –-each l corresponds to a different suborbital shape or suborbital type within an n-level If n=1, then l = 0 can only exist (s only) If n=2, then l = 0 or 1 can exist (s and p) If n=3, then l = 0, 1, or 2 can exist (s, p and d)

28 Atomic suborbital s orbitals are spherically symmetric s orbital properties: one s orbital for every n-level: l = 0

29 The three p-orbitals lie 90 o apart in space There are 3 p-orbitals for every n-level (when n ≥ 2): l = 1 p Orbital

30 Magnetic Quantum Number (m l ) m l = - l, (- l + 1), (- l +2),.....0, , ( l -2), ( l -1), + l –Example: m l for l = 0, 1, 2, 3, … l –0, , , , …+ l through – l -This describes the number of suborbitals and direction each suborbital faces within a given subshell ( l ) within an orbital (n) -There is no energy difference between each suborbital (m l ) set –If l = 0 (or an s orbital), then m l = 0 for every n Notice that there is only 1 value of m l. This implies that there is one s orbital per n value, when n  1 –If l = 1 (or a p orbital), then m l = -1, 0, +1 for n-levels >2 There are 3 values of m l for p suborbitals. Thus there are three p orbitals per n value, when n  2

31 Atomic suborbital s orbitals are spherically symmetric s orbital properties: one s orbital for every n-level: l = 0 and only 1 value for m l

32 p Orbital Properties The first p orbitals appear in the n = 2 shell -p orbitals have peanut or dumbbell shaped volumes -They are directed along the axes of a Cartesian coordinate system. There are 3 p orbitals per n-level: –-The three orbitals are named p x, p y, p z. –-They all have an l = 1 with different m l –-m l = -1, 0, +1 (are the 3 values of m l )

33 When n = 2, then l = 0 and/or 1 Therefore, in n = 2 shell there are 2 types of suborbitals/subshells For l = 0m l = 0 this is an s subshell this is an s subshell For l = 1 m l = -1, 0, +1 this is a with this is a p subshell with 3 orientations When n = 2, then l = 0 and/or 1 Therefore, in n = 2 shell there are 2 types of suborbitals/subshells For l = 0m l = 0 this is an s subshell this is an s subshell For l = 1 m l = -1, 0, +1 this is a with this is a p subshell with 3 orientations When l = 1, there is a single PLANAR NODE thru the nucleus p orbitals are peanut or dumbbell shaped p Orbitals

34 d Orbital Properties The first d suborbitals appear in the n = 3 shell -The five d suborbitals have two different shapes: – 4 are clover shaped – 1 is dumbbell shaped with a doughnut around the middle -The suborbitals lie directly on the Cartesian axes or are rotated 45 o from the axes There are 5d orbitals per n level: – The five orbitals are named – They all have an l = 2 with different m l m l = -2,-1,0,+1,+2 (5 values of m l )

35 s orbitals l = 0, have no planar node, and so are spherical p orbitals l = 1, have 1 planar node, and so are “dumbbell” shaped This means d orbitals with l = 2, have 2 planar nodes, and so have 2 different shapes (clover and dumbbell with a donut) Figure 7.16 d Orbitals

36 d Orbital Shape

37 f Orbitals There are 7 f orbitals with l =3 m l = -3, -2,-1,0,+1,+2, +3 (7 values of m l ) -These orbitals are hard to visualize or describe

38 When n = 4, l = 0, 1, 2, 3 so there are 4 subshells in this orbital (energy level) For l = 0, m l = 0 ---> s subshell with single suborbital ---> s subshell with single suborbital For l = 1, m l = -1, 0, > p subshell with 3 suborbitals ---> p subshell with 3 suborbitals For l = 2, m l = -2, -1, 0, +1, > d subshell with 5 suborbitals ---> d subshell with 5 suborbitals For l = 3, m l = -3, -2, -1, 0, +1, +2, > f subshell with 7 suborbitals ---> f subshell with 7 suborbitals f Orbitals

39 One of 7 possible f orbitals All have 3 planar surfaces f Orbital Shape

40 Spin Quantum Number (m s ) Describes the direction of the spin the electron has only two possible values: m s = +1/2 or -1/2 m s = ± 1/2 proven experimentally that electrons have spins

41 Spin Quantum Number Spin quantum number effects: Every orbital can hold up to two electrons Why? The two electrons are designated as having: one spin up  and one spin down   Spin describes the direction of the electron’s magnetic fields

42 Electron Spin and Magnetism Diamagnetic: NOT attracted to a magnetic field -they are repelled by magnetic fields -no unpaired electrons Paramagnetic: are attracted to a magnetic field -unpaired electrons