5 Electromagnetic Radiation Relating frequency and wavelengthc = l . nc = l . fc = speed of light = 3.00 x 108 m/sn or f = frequency in cycle per second or Hertz= wavelength in meters(1 nm = 1 x 10-9 m)Note: As wavelength increases, frequency (& energy) will decrease.
6 Limitations of the Wave Model of Light The prevailing laws of physics couldn’t explain:Blackbody Radiation – emission of light from hot objectsPhotoelectric Effect – emission of electrons from metal surfaces on which light strikesEmission Spectra – emission of light from excited gas atoms*Couldn’t relate temperature , intensity, & wavelength of light
7 Max Planck 1900Solved problem by stating energy can only be released or absorbed in discrete ‘chunks’ of some minimum size.He named this smallest quantity of energy a ‘quantum’.He said the minimum amount of energy that an object can gain or lose is related to its frequency.E = h . fE = Energy in Joulesh = Planck’s Constant = x Joule-secondf = frequency in cycles per second or Hertz
8 Albert Einstein 1905Used Planck’s Quantum Theory to explain the photoelectric effect.Photoelectric Effect - light shining on a clean metal surface causes the surface to emit electrons if the light is of a certain minimum frequency .He said light energy hitting a metal surface is not like a wave but like a stream of tiny energy packets called ‘photons’.He said the energy of a photon can also be found by:E = h * f6. No matter the intensity, if the photons don’t have enough energy, no electrons are emitted.
9 Dual Nature of LightPlanck & Einstein are describing light as behaving like tiny particles of energy – just like matter is made of particles!We theorize light has both a wave like and a particle like nature.We refer to this as the DUAL NATURE OF LIGHT.
10 Bohr Model of the AtomGround State = when electrons are in the lowest energy stateExcited State – when electrons absorb energy & move to a higher energy stateSpectra – light energy given off when electrons return to lower energy statesLIMITATION: Bohr couldn’t explain spectra of multi-electron atoms.
11 Red, Orange, Yellow, Green, Blue, Indigo, Violet RecallHot objects give off light.When the light from a light bulb passes through a prism, a RAINBOW or CONTINUOUS SPECTRUM forms.Remember ROY G. BIV?Red, Orange, Yellow, Green, Blue, Indigo, Violet
12 When the light from an element gas tube passes through a prism, only some colors are seen – called a BRIGHT-LINE SPECTRUM or LINE SPECTRA.Gas TubeHydrogen gas gives off pink lightPower SupplyHydrogen’s Bright Line Spectrum as viewed through a prism
13 This site shows the Line Spectra of Various Elements Often Shown This WayThis site shows the Line Spectra of Various Elements
14 1/l = (RH)( 1/n12 - 1/n22 ) Johann Balmer Showed that the wavelengths of the four visiblelines of hydrogen fit the following formula:1/l = (RH)( 1/n /n22 )Where RH = Rydberg ConstantRH = x 107 m-1n = energy level(n2 bigger than n1)
15 Niels Bohr explains Hydrogen’s Line Specta Bohr’s PostulatesElectrons must be in specific energy levelsAn electron in an allowed energy state will not radiate energy & spiral into the nucleusEnergy is emitted or absorbed by electrons as they move from one allowed energy state to another.The amount of energy: E = h . f
16 n is the energy level or principal quantum number How much energy?Bohr calculated the energy an electron possesses when in each energy state.E = (-2.18 x J) (1/n2)where n = 1, 2, 3, etc.n is the energy level or principal quantum numberNote that the values are negative. The energy is lowest (most negative) for n = 1.When the electron is completely removed and an ion forms the energy = zero.
18 And the Energy Change? DE = (-2.18 x 10-18 J) (1/nf2 - 1/ni2) Where the initial energy state = niWhere the final energy state = nf
19 Dual Nature of Light & Matter! Light has both particle (photon) & wavelike properties.Louis de Broglie suggested that matter is the same – called the de Broglie’s hypothesis.Matter has both particle like & wave like properties.
20 De Broglie’s Hypothesis For matter waves:= h / (m . v)Where: l = wavelength (meters)m v = momentumm = mass (kg)v = velocity (m/s)h = x Joule-secondRecall: Joule = 1 kg-m2/s2This wavelength only becomes significant when dealing with tiny high velocity particles such as electrons.
21 Heisenberg’s Uncertainty Principle Heisenberg’s Uncertainty Principle: It is inherently impossible for us to know simultaneously both the exact momentum of an object and its exact location in space.This becomes significant when dealing with the position of electrons within an atom.
22 QUANTUM MECHANICSLIMITATION: Bohr couldn’t explain spectra of multi-electron atoms.It took Quantum Mechanics to explain the behavior of light emitted by multi-electron atoms.Quantum Mechanics is one of the most revolutionary discoveries of the 20th century – the ‘new’ physics.
23 Quantum MechanicsHeisenberg & de Broglie set the stage for a new model of the electron that would describe its location not precisely, but in terms of probabilities - called Quantum Mechanics or Wave Mechanics.
24 Erwin Schrodinger (1887 – 1961)Proposed a Wave Equation (wave functions - y) that incorporates the dual nature of the electron.Y2 provides info about the electron’s location.In the Quantum Mechanical Model, we speak of the probability (Y2) that the electron will be in a certain region of space at a given instant.We call it probability density or electron density.
25 Con’t4) The wave functions are called orbitals. 5) Orbitals differ in energy, shape, and size. 6) An orbital can hold up to TWO electrons. 7) Four numbers can be used to describe the location of an electron in an orbital.
26 Four Quantum Numbers 1st Quantum Number = The Principal Quantum Number (n)2nd Quantum Number =The Azimuthal Quantum Number orThe Angular Momentum Quantum Number (l)3rd Quantum Number =The Magnetic Quantum Number (ml)4th Quantum Number =The Spin Magnetic Quantum Number (ms)
27 Pauli Exclusion Principle Pauli Exclusion Principle states that no two electrons in an atom can have the same set of 4 quantum numbers. ( n, l, ml , ms )
28 1st Quantum NumberIt tells the principal energy level (shell) – ‘n’ n = 1 for the 1st PEL n = 2 for the 2nd PEL , etc. As the value of ‘n’ increases, the electron has more energy, is less tightly bound to the nucleus, and it spends more time further away from the nucleus.
29 2nd Quantum NumberIt tells the sublevel or subshell, which indicates the shape of the orbital – ‘l’If ‘l’ = zero, the sublevel is sIf ‘l’ = 1, the sublevel is pIf ‘l’ = 2, the sublevel is dIf ‘l’ = 3, the sublevel is fIn terms of energy, s < p < d < f.The value of ‘l’ is always at least one less than the value of ‘n’.
30 3 rd Quantum Number ml ml ml ml ml It tells the orientation of the orbital in the sublevel - For the s sublevel, there is only one orientation: = 0 For the p sublevel, there are 3 possible orientations: = +1, 0, -1 For the d sublevel, there are 5 possible orientations: = +2, +1, 0, -1, -2 For the f sublevel, there are 7 possible orientations: = +3, +2, +1, 0, -1, -2, -3mlmlmlmlml
31 4th Quantum NumberIt tells the electron spin within the orbital There are two possible values: + 1/2 or – 1/2 They indicate the two opposite directions of electron spin – which produce oppositely directed magnetic fields.(ms)
45 Be Able To:Assign a set of four quantum number to each electron in an atom.Recognize a valid set of quantum numbersDescribe atomic orbitals using quantum numbers.Determine the # of orbitals and/or electrons in a given energy level or sublevel.State the order of orbital energies from highest to lowest.
48 Table 7-2: Electron Configuration and Energy Levels for the Periodic Table of the Elements Group123456789101112131415161718Periods-Orbitalsd-Orbitalsp-Orbitals1s11s22s12s22p12p22p32p42p52p63s13s23p13p23p33p43p53p64s14s23d13d23d33d43d53d63d73d83d93d104p14p24p34p44p54p65s15s24d14d24d34d44d54d64d74d84d94d105p15p25p35p45p55p66s16s2*5d15d25d35d45d55d65d75d85d95d106p16p26p36p46p56p67s17s2**6d16d26d36d46d56d66d76d86d96d107p17p27p37p47p57p6f-Orbitals* Lanthanoids4f14f24f34f44f54f64f74f84f94f104f114f124f134f14** Actinoids 5f15f25f35f45f55f65f75f85f95f105f115f125f135f14
49 Orbital NotationOne way: NitrogenAnother way: Aluminum
50 Pauli Exclusion Principle Pauli Exclusion Principle states that no two electrons in an atom can have the same set of 4 quantum numbers. ( n, l, ml , ms ) NO! YES!
51 Hund’s RuleHund’s Rule – For degenerate orbitals, minimum energy is obtained when the number of electrons with the same spin is maximized.Degenerate – means same sublevel