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CHAPTER 6. The Structure of Atoms. Figure 7.1. Electromagnetic Radiation. Mathematical theory that describes all forms of radiation as oscillating (wave-like) electric and magnetic fields. Wave Properties. Wavelength ( l ): distance between consecutive crests or troughs Frequency ( n ):
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CHAPTER 6 • The Structure of Atoms
Figure 7.1 Electromagnetic Radiation Mathematical theory that describes all forms of radiation as oscillating (wave-like) electric and magnetic fields
Wave Properties Wavelength (l): distance between consecutive crests or troughs Frequency (n): 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 l/2 Amplitude Node (l/2) wavelength
Wave Properties • c = for electromagnetic radiation Speed of light (c): 2.99792458 x 108 m/s Example: What is the frequency of green light of wavelength 5200 Å?
Electromagnetic Spectrum wavelength increases energy increases frequency increases?
Planck’s Equation E = h • Maxwell Planck h = Planck’s constant = 6.6262 x 10-34 J•s Any object can gain or lose energy by absorbing or emitting radiant energy -only certain vibrations (n) are possible (Quanta) -Energy of radiation is proportional to frequency (n)
Planck’s Equation Maxwell Planck E = h • =hc/l Light with large (small ) has a small E Light with a short (large ) has a large E
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?
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)
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
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
final int Atomic Spectra • Balmer equation (Rydberg equation):relates the wavelengths of the lines (colors) in the atomic spectrum Principle quantum number
Atomic Spectra What is the wavelength of light emitted when the hydrogen atom’s energy changes from n = 4 to n = 2? nfinal = 2 ninitial = 4
The Bohr Model Bohr’s greatest contribution to science was in building a simple model of the atom It was based on an understanding of theSHARP LINE EMISSION SPECTRAof excited atoms Niels Bohr (1885-1962)
The Bohr Model Early view of atomic structure from the beginning of the 20th century -electron (e-) traveled around the nucleus in an orbit 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 - - -
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...
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)
Atomic Spectra and Niels Bohr 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 (1885-1962)
Wave Properties of the Electron de Broglie (1924) proposed that all moving objects have wave properties For light: E = mc2 E = h = hc/ Therefore, mc = h/ For particles: (mass)(velocity) = h/ Louis de Broglie (1892-1987)
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:
The Wave Nature of the Electron Determine the wavelength, in meters, of an electron, with mass 9.11 x 10-31 kg, having a velocity of 5.65 x 107 m/s Remember Planck’s constant is 6.626 x 10-34 J s which is also equal to 6.626 x 10-34 kg m2/s, because 1 J = 1 kg m2/s2
200 pm . 50 pm 0 200 100 r (pm) Quantum (Wave) Mechanics 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 Y describes an allowed energy state for an e- and gives the probability (Y2) of the location for the e- Quantization is introduced naturally Erwin Schrödinger 1887-1961 y2
Uncertainty Principle The problem with defining the nature of electrons in atoms was solved by W. Heisenberg the position and momentum (momentum = m•v)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 Werner Heisenberg 1901-1976 n-levels
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)
The Principal Quantum Number (n) 8 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)
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)
Atomic suborbital • s orbitals are spherically symmetric • s orbital properties: • one s orbital for every n-level: l = 0
p Orbital The three p-orbitals lie 90o apart in space • There are 3 p-orbitals for every n-level (when n ≥ 2): • l = 1
Magnetic Quantum Number (ml) ml= - l , (- l + 1), (- l +2), .....0, ......., (l -2), (l -1), +l • Example:ml for l = 0, 1, 2, 3, …l • 0, +1 0 -1, +2 +1 0 -1 -2, +3 +2 +1 0 -1 -2 -3, …+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 (ml) set • Ifl = 0 (or an s orbital), then ml = 0 for every n • Notice that there is only 1 value of ml. This implies that there is one s orbital per n value, when n 1 • Ifl = 1 (or a p orbital), then ml = -1, 0, +1 for n-levels >2 • There are 3 values of ml for p suborbitals. Thus there are three p orbitals per n value, when n 2
Atomic suborbital • s orbitals are spherically symmetric • s orbital properties: • one s orbital for every n-level: l = 0 and only 1 value for ml
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 px, py, pz. • -They all have anl = 1 with different ml • -ml = -1, 0, +1 (are the 3 values of ml)
p Orbitals When n = 2, then l = 0 and/or 1 Therefore, in n = 2 shell there are 2 types of suborbitals/subshells For l = 0 ml = 0 this is an s subshell For l = 1 ml = -1, 0, +1 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
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 45o from the axes There are 5d orbitals per n level: • The five orbitals are named • They all have an l = 2 with different ml • ml = -2,-1,0,+1,+2 (5 values of ml)
Figure 7.16 d Orbitals 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)
f Orbitals • There are 7 f orbitals with l=3 • ml = -3, -2,-1,0,+1,+2, +3 (7 values of ml) -These orbitals are hard to visualize or describe
f Orbitals When n = 4, l = 0, 1, 2, 3 so there are 4 subshells in this orbital (energy level) For l = 0, ml = 0 ---> s subshell with single suborbital For l = 1, ml = -1, 0, +1 ---> p subshell with 3 suborbitals For l = 2, ml = -2, -1, 0, +1, +2 ---> d subshell with 5 suborbitals For l = 3, ml = -3, -2, -1, 0, +1, +2, +3 ---> f subshell with 7 suborbitals
f Orbital Shape One of 7 possible f orbitals All have 3 planar surfaces
Spin Quantum Number (ms) Describes the direction of the spin the electron has only two possible values: ms = +1/2 or -1/2 ms = ± 1/2 proven experimentally that electrons have spins
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
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 Electron Spin and Magnetism