ATOMIC STRUCTURE Kotz Ch 7 & Ch 22 (sect 4,5) properties of light spectroscopy quantum hypothesis hydrogen atom Heisenberg Uncertainty Principle orbitals

ELECTROMAGNETIC RADIATION subatomic particles (electron, photon, etc) have both PARTICLE and WAVE properties Light is electromagnetic radiation - crossed electric and magnetic waves: Properties : Wavelength, l (nm) Frequency, n (s-1, Hz) Amplitude, A constant speed. c 3.00 x 108 m.s-1

Electromagnetic Radiation (2)

Electromagnetic Radiation (3) All waves have: frequency and wavelength symbol: n (Greek letter “nu”) l (Greek “lambda”) units: “cycles per sec” = Hertz “distance” (nm) All radiation: l • n = c where c = velocity of light = 3.00 x 108 m/sec Note: Long wavelength  small frequency Short wavelength  high frequency increasing wavelength frequency

Electromagnetic Radiation (4) Example: Red light has l = 700 nm. Calculate the frequency, n. = 3.00 x 10 8 m/s 7.00 x 10 -7 m 4.29 x 10 14 Hz n = c l Wave nature of light is shown by classical wave properties such as interference diffraction

Quantization of Energy Max Planck (1858-1947) Solved the “ultraviolet catastrophe” 4-HOT_BAR.MOV Planck’s hypothesis: An object can only gain or lose energy by absorbing or emitting radiant energy in QUANTA.

Quantization of Energy (2) Energy of radiation is proportional to frequency. E = h • n where h = Planck’s constant = 6.6262 x 10-34 J•s Light with large l (small n) has a small E. Light with a short l (large n) has a large E.

Photoelectric Effect Albert Einstein (1879-1955) Photoelectric effect demonstrates the particle nature of light. (Kotz, figure 7.6) No e- observed until light of a certain minimum E is used. Number of e- ejected does NOT depend on frequency, rather it depends on light intensity.

Photoelectric Effect (2) Classical theory said that E of ejected electron should increase with increase in light intensity — not observed! Experimental observations can be explained if light consists of particles called PHOTONS of discrete energy.

Energy of Radiation PROBLEM: Calculate the energy of 1.00 mol of photons of red light. l = 700 nm n = 4.29 x 1014 sec-1 E = h•n = (6.63 x 10-34 J•s)(4.29 x 1014 sec-1) = 2.85 x 10-19 J per photon E per mol = (2.85 x 10-19 J/ph)(6.02 x 1023 ph/mol) = 171.6 kJ/mol - the range of energies that can break bonds.

Atomic Line Spectra 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 (1885-1962) (Nobel Prize, 1922)

Line Spectra of Excited Atoms Excited atoms emit light of only certain wavelengths The wavelengths of emitted light depend on the element. H Hg Ne

Atomic Spectra and Bohr Model One view of atomic structure in early 20th century was that an electron (e-) traveled about the nucleus in an orbit. 1. Classically any orbit should be possible and so is any energy. 2. But a charged particle moving in an electric field should emit energy. End result should be destruction!

Atomic Spectra and Bohr Model (2) Bohr said classical view is wrong. Need a new theory — now called QUANTUM or WAVE MECHANICS. e- can only exist in certain discrete orbits — called stationary states. e- is restricted to QUANTIZED energy states. Energy of state = - C/n2 where C is a CONSTANT n = QUANTUM NUMBER, n = 1, 2, 3, 4, ....

Atomic Spectra and Bohr Model (3) Energy of quantized state = - C/n2 Only orbits where n = integral number are permitted. Radius of allowed orbitals = n2 x (0.0529 nm) Results can be used to explain atomic spectra.

Atomic Spectra and Bohr Model (4) If e-’s are in quantized energy states, then DE of states can have only certain values. This explains sharp line spectra. H atom 07m07an1.mov n = 1 n = 2 E = -C (1/22) E = -C (1/12) 4-H_SPECTRA.MOV

Atomic Spectra and Bohr Model (5) . Atomic Spectra and Bohr Model (5) n = 1 2 Energy Calculate DE for e- in H “falling” from n = 2 to n = 1 (higher to lower energy) . DE = Efinal - Einitial = -C[(1/12) - (1/2)2] = -(3/4)C (-ve sign for DE indicates emission (+ve for absorption) since energy (wavelength, frequency) of light can only be +ve it is best to consider such calculations as DE = Eupper - Elower C has been found from experiment. It is now called R, the Rydberg constant. R = 1312 kJ/mol or 3.29 x 1015 Hz so, E of emitted light = (3/4)R = 2.47 x 1015 Hz and l = c/n = 121.6 nm (in ULTRAVIOLET region) This is exactly in agreement with experiment!

n En = -1312 n2 High E Short l High n Low E Long l Low n Hydrogen atom spectra Visible lines in H atom spectrum are called the BALMER series. 6 5 3 2 1 4 n Energy Ultra Violet Lyman Visible Balmer Infrared Paschen En = -1312 n2

From Bohr model to Quantum mechanics Bohr’s theory was a great accomplishment and radically changed our view of matter. But problems existed with Bohr theory — theory only successful for the H atom. introduced quantum idea artificially. So, we go on to QUANTUM or WAVE MECHANICS

Quantum or Wave Mechanics Light has both wave & particle properties de Broglie (1924) proposed that all moving objects have wave properties. For light: E = hn = hc / l For particles: E = mc2 (Einstein) L. de Broglie (1892-1987) Therefore, mc = h / l and for particles (mass)x(velocity) = h / l l for particles is called the de Broglie wavelength

WAVE properties of matter Na Atom Laser beams l = 15 micometers (mm) Andrews, Mewes, Ketterle M.I.T. Nov 1996 The new atom laser emits pulses of coherent atoms, or atoms that "march in lock-step." Each pulse contains several million coherent atoms and is accelerated downward by gravity. The curved shape of the pulses was caused by gravity and forces between the atoms. (Field of view 2.5 mm X 5.0 mm.) WAVE properties of matter Electron diffraction with electrons of 5-200 keV - Fig. 7.14 - Al metal Davisson & Germer 1927 4-ATOMLSR.MOV

Quantum or Wave Mechanics Schrodinger applied idea of e- behaving as a wave to the problem of electrons in atoms. Solution to WAVE EQUATION gives set of mathematical expressions called WAVE FUNCTIONS, Y Each describes an allowed energy state of an e- Quantization introduced naturally. E. Schrodinger 1887-1961

WAVE FUNCTIONS, Y • Y is a function of distance and two angles. • For 1 electron, Y corresponds to an ORBITAL — the region of space within which an electron is found. • Y does NOT describe the exact location of the electron. • Y2 is proportional to the probability of finding an e- at a given point.

Uncertainty Principle Problem of defining nature of electrons in atoms solved by W. Heisenberg. Cannot simultaneously define the position and momentum (= m•v) of an electron. Dx. Dp = h At best we can describe the position and velocity of an electron by a PROBABILITY DISTRIBUTION, which is given by Y2 W. Heisenberg 1901-1976

Y2 is proportional to the probability Wavefunctions (3) Y2 is proportional to the probability of finding an e- at a given point. 4-S_ORBITAL.MOV (07m13an1.mov)

Orbital Quantum Numbers An atomic orbital is defined by 3 quantum numbers: n l ml Electrons are arranged in shells and subshells of ORBITALS . n  shell l  subshell ml  designates an orbital within a subshell

Symbol Values Description Quantum Numbers Symbol Values Description n (major) 1, 2, 3, .. Orbital size and energy = -R(1/n2) l (angular) 0, 1, 2, .. n-1 Orbital shape or type (subshell) ml (magnetic) -l..0..+l Orbital orientation in space Total # of orbitals in lth subshell = 2 l + 1

Shells and Subshells For n = 1, l = 0 and ml = 0 There is only one subshell and that subshell has a single orbital (ml has a single value ---> 1 orbital) This subshell is labeled s (“ess”) and we call this orbital 1s Each shell has 1 orbital labeled s. It is SPHERICAL in shape.

s Orbitals All s orbitals are spherical in shape.

p Orbitals Typical p orbital For n = 2, l = 0 and 1 There are 2 types of orbitals — 2 subshells For l = 0 ml = 0 this is a s subshell For l = 1 ml = -1, 0, +1 this is a p subshell with 3 orbitals planar node When l = 1, there is a PLANAR NODE through the nucleus.

p orbitals (2) The three p orbitals lie 90o apart in space A p orbital

px py pz l = p-orbitals(3) n= 2 3

d Orbitals l = 0, 1, 2 For l = 1, ml = -1, 0, +1 For n = 3, what are the values of l? l = 0, 1, 2 and so there are 3 subshells in the shell. For l = 0, ml = 0  s subshell with single orbital For l = 1, ml = -1, 0, +1  p subshell with 3 orbitals For l = 2, ml = -2, -1, 0, +1, +2  d subshell with 5 orbitals

d Orbitals IN GENERAL the number of NODES = value of angular typical d orbital planar node s orbitals have no planar node (l = 0) and so are spherical. p orbitals have l = 1, and have 1 planar node, and so are “dumbbell” shaped. d orbitals (with l = 2) have 2 planar nodes IN GENERAL the number of NODES = value of angular quantum number (l)

Boundary surfaces for all orbitals of the n = 1, n = 2 and n = 3 shells There are n2 orbitals in the nth SHELL 2 1

ATOMIC ELECTRON CONFIGURATIONS AND PERIODICITY

Element Mnemonic Competition Hey! Here Lies Ben Brown. Could Not Order Fire. Near Nancy Margaret Alice Sits Peggy Sucking Clorets. Are Kids Capable ? WHAT’s YOURs ??