Arrangement of Electrons in Atoms

Electrons in Atoms

1

Wave description of light

Electromagnetic spectrum - made of electromagnetic radiation (forms of energy that exhibit wavelike behavior as they travel through space).Electromagnetic waves - combination of electrical and magnetic fields which travel at the speed of light c = 3.00 x 108 m/sec

2Wavelength (lambda) usually measured in nm or ngstroms ()

3Relative sizes of wavelengths

4Frequency

Frequency (Greek letter nu) (or f) units are usually cycles/sec, sec 1, or Hertz (Hz).5c = = 3.0 x 108 m/sec

www.atmos.washington.edu/~hakim/301/handouts.html

6The Photoelectric effectThe emission of electrons from ametal when lightshines on themetal. The number of electrons and theirenergies dependson the brightnessof the incidentlight.

http://www.astro.virginia.edu/class/oconnell/astr30/im/photoelectric-effect-2.jpg7Max Planck (1900)He suggested that the object emits energy in small, specific amounts called quanta. A quantum is the minimum quantity of energy that can be lost or gained by an atom. He proposed E = h where E = energy in Joules, = frequency , and h = Plancks constant; 6.626 x 10-34 Js

E = h 8What is a Joule?

James Prescott JouleA Joule is the derived unit of energy in the SI system. It is the energy exerted by a force of one Newton acting to move an object through a distance of one meter.I Joule = Force x distance = 1 Newton-meter = (mass x acceleration) x meter=kg m/s2 m = kgm2/s2

Einstein and wave-particle duality (1905)abyss.uoregon.edu/~js/images/wave_particle.gif

10Light particle and wave?Each particle of lightcarries a quantum ofenergy which Einsteincalled photons. A photon isa particle of electromagneticradiation having zero massand carrying a quantum ofenergy.

For an electron to be ejected from the surface of a metal, the metal surface must be hit by a single photon possessing at least the minimum energy required to knock the electron loose (multiples of whole numbers of photons) Each metal has electrons bound to its surface with different strengths so the minimum frequencies differ with each metal. 11Spectroscopy

12The Hydrogen-atom Bright Line-Emission Spectrum

13Energy of photons emittedWhen an excited hydrogen atom falls backfrom an excited state (a higher potentialenergy than it has in its ground state) to itsground state (lowest energy state of anatom) or a lower energy state, it emits aphoton of radiation. Ephoton = E2-E114Bohr (Niels) Model of the Atom - 1913

15Evidence for Electrons in Fixed-Energy Levels

The collection of narrow bands of light energy is referred to as an emission line spectrum, and the individual bands of light are called spectral lines.

The concept of electron energy levels is supported by spectral lines.

16Combining equationsGiven: E = h and E = E2-E1 combining them results in = E = ( RH) (1 - 1 ) h h n2i n2fFurther simplification:

E = ( RH) (1 - 1 ) n2i n2f

17Bohr Model of the atomElectrons in hydrogen atoms exist in only specified energy states.Electrons in hydrogen atoms can absorb only certain specific amounts of energy and no others.When the excited electrons in a hydrogen atom lose energy, they lose only specific amounts of energy as photons.Different photons produce different color lines as seen in a bright line-emission spectrum. The main problem was that this explanation could not explain the behavior of any other element besides hydrogen.

18What led to quantum theory?The visible bands in aspectra are called theBalmer series. The UVand IR lines are calledLyman and Paschenseries, respectively.Scientists expected tosee a continuousspectrum.This observation of thehydrogen atom led toquantum theory.

19If electrons behave as both particles and waves, where are they located in an atom?

20Heisenberg Uncertainty Principle (1927)It is impossible to determine simultaneously boththe position and velocity of an electron or anyother particle. (p) ( x) = h (Plancks constant)p = uncertainty in momentumx = uncertainty in position

21The Quantum Model of the Atom

1924 Louis de BroglieElectrons should beconsidered as wavesconfined to the spacearound the nucleus.

http://youtube.com/watch?v=x_tNzeouHC4Bohr applet:http://www.colorado.edu/physics/2000/quantumzone/bohr.html

22Derivation of the de Broglie wavelength equationEinsteinPlanckE = mc2E = h Therefore:mc2 = h [Substitute v (any velocity) for c] mv2 = h [rearrange and substitute v for c in c = ; then solve for = v ] mv2 = hv Substitute, rearrange, solve for = hv and simplify even further: mv2

= h This is the de Broglie wavelength mv equation23Germer and DavissonDe Broglies equation was applicable to anyobject, not just atoms. The wave propertiesof electrons were demonstrated in 1927 by Germer and Davisson (U.S.) usingdiffraction by crystals.

This technique is used today in electron microscopy.

See the following website for details on what they did. http://dev.physicslab.org/Document.aspx?doctype=3&filename=AtomicNuclear_DavissonGermer.xml

24Erwin Schrdinger and thewave mechanical model

( + + ) + 82m (E-V) = 0 x2 y2 z2 h2

(psi) = wave amplitude functionm = mass of electronE = energyV = potential energyx, y, and z are the coordinates in space where the equation is solved

25Wave functions = orbitalsThe solutions to his equation areknown as wave functions andthey describe the regions in spacewhere there is a high probability offinding the electron at the point inspace for which the equation wassolved. These regions of space arecalled orbitals.

26Quantum numbersDescribe the properties of atomic orbitals and theproperties of electrons in these orbitals. There are4 quantum numbers, the first three of whichresult from the solutions to Schrdingers waveequation.

Principal quantum number (n) the main energylevel occupied by the electron. n= 1,2,3,4, . . .The total number of orbitals within a given shell isequal to n2. The total number of electrons within agiven shell is equal to 2n2.

27Orbital (or azimuthal) quantum number (l) or angular momentum quantum numberValues include l = 0, up to and including n-1The letter designations originally stood for sharp,principal, diffuse and fundamental. These words were used to describe different series of spectral linesemitted by the elements.

Orbital quantum number

Letter designation

Number of orbitals

Number of electrons per sublevel

0s121p362d5103f71428Magnetic and spin quantum numbersMagnetic quantum number (ml) indicates theorientation of an orbital around the nucleus.Values range from l to +l (defines how many ofeach type of orbital exists)Spin quantum number (ms) indicates the twopossible spin states of electrons in orbitals. Values are either + or

29Principal quantum numberOrbital quantum numberMagnetic quantum number

Spin quantum numbersEither clockwise (+ ) or counterclockwise (- )n = 1l = 0 (s) ml = 0 + , n = 2l = 0 (s), l = 1 (p)ml = 0ml = -1, 0, +1 + , + , ; + , ; + , n = 3l = 0 (s), l = 1 (p),l = 2 (d)ml = 0ml = -1, 0, +1ml = -2, -1, 0, +1, +2+ , + , : + , ; + , + , ; + , ; + , ; + , ; + , n = 4l = 0 (s), l = 1 (p),l = 2 (d),l = 3 (f)ml = 0ml = -1, 0, +1ml = -2, -1, 0, +1, +2ml = -3, -2, -1, 0, +1, +2, +3+ , + , ; + , ; + , + , ; + , ; + , ; + , ; + , + , ,; + , ; + , ; + , ; + , ; + , ; + , 30s orbital

31p orbitals

32d orbitals

33f orbitals

34Electron configuration notationLong hand configuration (always start with 1s)Short hand, or noble gas configuration (use the noble gas immediately preceding the element in question, put its symbol in brackets [ ], and then write out the outer shell configuration.Orbital diagram/notation configuration

35Electron configurations- rulesAufbau principle:An electron occupies thelowest energyorbital that canreceive it.

Diagonal Rule

36

Order of orbital fillingEnergy in orbital filling

Hunds Ruleorbitals of equalenergy are each occupied by one electron before anyorbital is occupied bya second electron, andall electrons in singly occupied orbitalsmust have the samespin.

Pauli Exclusion principleno two electrons in the same atomhave the same set of four quantumnumbers. The first three may bethe same, but the spin must beopposite.

41Order of orbital fillinghttp://intro.chem.okstate.edu/WorkshopFolder/Electronconfnew.html

Example 1Boron atomic number 5Longhand: 1s22s22p1Shorthand: [He]2s22p1Orbital diagram:

1s 2s 2p

43Example 2Polonium atomic number 84Longhand: 1s22s22p63s23p64s23d104p65s24d105p66s24f145d106p4 Shorthand: [Xe] 6s24f145d106p4

Orbital diagram:

44Exceptions to the Aufbau principleFor Chromium (Cr) we would predict: 1s2 2s2 2p6 3s2 3p6 4s2 3d4 but it is actually -->1s2 2s2 2p6 3s2 3p6 4s13d5

For Copper (Cu)we would predict: 1s2 2s2 2p6 3s2 3p6 4s2 3d9 but it is actually --> 1s2 2s2 2p6 3s2 3p6 4s1 3d10

Degenerate orbitalsa group of orbitals with the same energyExamples: Chromium (24) CrShorthand: [Ar]4s13d5 NOT [Ar]4s23d4Mo and W are similar

Copper (29) CuShorthand: [Ar]4s13d10 NOT [Ar]4s23d9Ag and Au are similar

Additional DefinitionsParamagnetic: An atom has unpairedelectrons in its electron configuration.(Look at its orbital diagram)

Diamagnetic: All electrons in an atomare paired. (Look at its orbital diagram)

Ion ConfigurationsElectrons will be added to, or taken away fromorbitals in the following order: s, p, d, f (i.e. the outer or valence shell first)Examples:Cl- 1s22s22p63s23p5 for Chlorine becomes 1s22s22p63s23p6Na+ 1s22s22p63s1 for sodium becomes 1s22s22p6