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

Electromagnetic Spectrum a.gov/kids/imagers/e ms/ a.gov/kids/imagers/e ms/ wh3KadEhttps:// wh3KadE

ELECTROMAGNETIC RADIATION subatomic particles (electron, photon, etc) have both PARTICLE and WAVE properties Light is electromagnetic radiation - crossed electric and magnetic waves: Properties : Wavelength,  (nm) Frequency,  (s -1, Hz) Amplitude, A constant speed. c 3.00 x 10 8 m.s -1

Electromagnetic Radiation (2)

All waves have: frequency and wavelength symbol:  Greek letter “nu”)   Greek “lambda”) units: “cycles per sec” = Hertz“distance” (nm) All radiation:  = c where c = velocity of light = 3.00 x 10 8 m/sec Electromagnetic Radiation (3) Note: Long wavelength  small frequency Short wavelength  high frequency increasing wavelength increasing frequency

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

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

E = h Quantization of Energy (2) Energy of radiation is proportional to frequency. where h = Planck’s constant = x Js Light with large (small ) has a small E. Light with a short (large ) has a large E.

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

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

E = h E = h = (6.63 x Js)(4.29 x sec -1 ) = (6.63 x Js)(4.29 x sec -1 ) = 2.85 x J per photon = 2.85 x J per photon Energy of Radiation PROBLEM: Calculate the energy of 1.00 mol of photons of red light.  = 700 nm = 4.29 x sec -1 - the range of energies that can break bonds. E per mol = (2.85 x J/ph)(6.02 x ph/mol) = kJ/mol

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 Niels Bohr ( ) (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 2. But a charged particle moving in an electric field should emit energy. 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. End result should be destruction! End result should be destruction!

Energy of state = - C/n 2 where C is a CONSTANT n = QUANTUM NUMBER, n = 1, 2, 3, 4,.... 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. Atomic Spectra and Bohr Model (2)

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

Hydrogen atom spectra Visible lines in H atom spectrum are called the BALMER series. High E Short Short High High Low E Long Long Low Low Energy Ultra Violet Lyman Infrared Paschen Visible Balmer E n = n n

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 From Bohr model to Quantum 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,  Each describes an allowed energy state of an e- Quantization introduced naturally. E. Schrodinger Quantum or Wave Mechanics

WAVE FUNCTIONS,   is a function of distance and two angles.  is a function of distance and two angles. For 1 electron,  corresponds to an ORBITAL — the region of space within which an electron is found. For 1 electron,  corresponds to an ORBITAL — the region of space within which an electron is found.  does NOT describe the exact location of the electron.  does NOT describe the exact location of the electron.  2 is proportional to the probability of finding an e- at a given point.  2 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 (= mv) of an electron.  x.  p = h At best we can describe the position and velocity of an electron by a  2 PROBABILITY DISTRIBUTION, which is given by  2 W. Heisenberg

Wavefunctions (3)  2 is proportional to the probability of finding an e- at a given point. 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: – nl l – n l m l Electrons are arranged in shells and subshells of ORBITALS. n  shell l  subshell m l  designates an orbital within a subshell

Quantum Numbers m l (magnetic)-l..0..+lOrbital orientation in space in space l (angular)0, 1, 2,.. n-1Orbital shape or type (subshell) type (subshell) n (major)1, 2, 3,..Orbital size and energy = -R(1/n 2 ) Total # of orbitals in l th subshell = 2 l + 1 SymbolValuesDescription

Shells and Subshells For n = 1, l = 0 and m l = 0 There is only one subshell and that subshell has a single orbital (m l 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 For n = 2, l = 0 and 1 There are 2 types of orbitals — 2 subshells For l = 0m l = 0 For l = 0m l = 0 this is a s subshell this is a s subshell For l = 1 m l = -1, 0, +1 For l = 1 m l = -1, 0, +1 this is a p subshell with 3 orbitals this is a p subshell with 3 orbitals planar node Typical p orbital When l = 1, there is a PLANAR NODE through the nucleus.

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

p-orbitals(3) pxpx pypy pzpz 2 3 n= l =

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

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 typical d orbital planar node 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 2 1 3d n= 3 There are n 2 orbitals in the n th SHELL

ATOMIC ELECTRON CONFIGURATIONS AND PERIODICITY