QUANTIZED ENERGY Energy comes in discrete packets or quanta Energy quantum of light h higher frequency higher energy where frequency of light h Planck s constant 6 63 x 10 34 Js Energy of a light beam can only be integer multiples of the quantum h E n h n 1 2 Dual Nature of Light wave c particle h hc shorter wavelength higher energy Experimental support black body radiation Planck 1900 photoelectric effect Einstein 1905 line spectra of hydrogen Bohr 1914 1 Spectroscopy study of light interacting with matter Spectrum distribution of in radiation Monochromatic light Single frequency no distribution in White light Continuous distribution of Hg vapor lamp Some discrete 519 549 688 741 821 1180 1630 GHz How can we explain this Is Hg the only atom that does this 2 Line spectra Hydrogen Neon 3 Line spectra of atoms 5 Excited state E3 Excited state E2 1 absorption E h 2 3 4 emission E h hc Ground state E 1 higher frequency higher energy shorter wavelength higher energy Observation of line spectra implies that atoms have discrete quantized energy levels 4 Bohr Model of H atom 1913 Electrons in fixed orbits eeeN 3rd orbit n 3 2nd orbit n 2 1st orbit n 1 1 En RH 2 n orbit n RH Rydberg constant 2 18x10 18 J n designates an electronic energy state of an H atom En is the energy level of an electronic state in an H atom En can be interpreted as the energy of an e in the nth orbit relative to a free e whose energy is defined 0 n 5 Bohr electronic energy 1 En RH 2 n Tells us the stability of an electronic state H atom as compared to the state without eMore negative value means more stable state The highest possible energy least stable state when n i e no e state or free e state E 0 Coulomb s Law helps when opposite charges come together they become stabilized by this much E Q1Q2 d Q1 charge of electron negative Q2 charge of proton positive d orbit radius distance between nucleus and electron Free remove an e from an orbit of H atom The atom becomes less stable the nucleus charge is no longer neutralized by e Energy is absorbed Energy of the atom becomes 0 E 0 Put a free e into the nth orbit of H atom initially the H atom has no electron i e E 0 The atom becomes more stable due to charge neutralization of nucleus by e Energy is given off Energy of the atom becomes negative En 6 Bohr Model of H atom 1913 Line spectrum is due to electronic transitions i e when an e changes its orbit H atom absorb or emit energy in the form of light when the atom changes its energy state when the e changes its orbit E final state energy initial state energy Ef Ei h 1 1 h E RH 2 2 ni nf where ni and nf are integers This predicts the H atom spectrum EXACTLY Note nf ni nf ni E is absorbs photon E is emits photon 7 Energy levels in Bohr Model 8 Bohr Model If ni 2 and nf 1 is energy emitted or absorbed 1 emitted 2 absorbed Of the following transitions in an Hatom which one results in the emission of the highest energy photon 1 2 3 4 5 n 1 n 6 n 6 n 3 n 3 n 6 n 1 n 4 n 6 n 1 9 Bohr Model If ni 2 and nf 1 what is the E change in the internal energy of H Would the atom emit or absorb light If ni 2 and nf 1 what is the wavelength in nm of the emitted photon E J how E is related to E h hc hc E 6 63 x 10 34 J s x 3 x 108 m s 1 6 x 10 18 J 1 24 x 10 7 m 1 24 x 10 7 m x 109 nm m 124 nm 10 Chapter 6 Part 2 Orbitals Quantum Numbers Many Electron Atoms Spin Quantum Number ms Pauli Exclusion Principle Hund s Rule Electron Configurations using the Periodic Table 11 From Orbits to Orbitals Bohr model explained some experimental evidence for hydrogen atom but it failed for other atoms DeBroglie 1924 if light has dual wave particle behavior perhaps matter does also Wavelength of matter waves h mv Electron waves discovered in 1927 Davidson and Garmer Basis for electron microscope For a baseball and bacteria is too small to observe but for electrons is of atomic size producing profound effects Electrons in atoms behave as standing waves Schr dinger equation 1926 Enter the Quantum World 12 Electron microscope Used to image some of the tiniest objects Image of HIV budding from T cell Electrons behave like light wave 13 Heisenberg Uncertainty Principle It is NOT possible to simultaneously know the position velocity momentum mv of a particle with complete certainty Derives from wavelike nature of matter This really becomes important when dealing with really small matter e g electrons All electrons have a velocity therefore you cannot specify their exact location It is not appropriate to imagine e moving in nice little orbits around the nucleus Contradicts Bohr s planetary model of the hydrogen atom Can we say anything about where the e are 14 Solutions of a Schr dinger equation for an electron paired with a proton wavefunctions H E x y z wavefunction describes a state of an electron no physical significance 2 x y z probability of finding one electron in a region of space also called probability density Heisenberg uncertainty principle It isn t possible to know the exact position and velocity momentum of particle simultaneously Think of electrons as clouds of electron density Orbitals x y z 15 What is an atomic orbital An atomic orbital is a 3 D wave Tells us WHERE an electron can be found in an atom Tells us the ENERGY of an electron in an atom Tells us the probability of finding an electron at a given point in an atom An orbital defines a value at every point in space When the values are plotted in space they form a 3D shape Contains information on the energy of an electron in an atom Designated by THREE quantum numbers 16 1 D standing waves frequency Classical waves nodes Increasing Energy node only certain stationary modes are allowed modes characterized by an integer nodes 1 for each dimension We need 1 number to designate a 1D wave more nodes in a wave higher frequency steeper slope of a wave higher energy multiple modes with equal energy degenerate appear in 2 3 D due to the symmetry of space 17 2 D standing waves We need 2 numbers to designate a 2D wave node 0 Increasing Energy No degeneracy node 1 degeneracy 2 node node 2 degenerate 18 3 D standing waves We need 3 numbers to designate a 3D wave Atomic orbitals are 3 D waves that define probability of finding an …