Electronic Structure and the Periodic Table

Electromagnetic Radiation Wave nature of light wavelength - l distance from the top (crest) of one wave to the top of the next wave units of distance - m,cm, Å 1 Å = 1 x 10-10 m = 1 x 10-8 cm frequency - u number of crests or troughs that pass a given point per second units of 1/time - s-1

Electromagnetic Radiation Speed of the wave, v Frequency multiplied by wavelength V = l u For light, speed = c relationship for electromagnetic radiation - c = l u c = velocity of light 3.00 x 108 m/s

Electromagnetic Radiation

Electromagnetic Radiation What is the frequency of green light of wavelength 5200 Å?

Electromagnetic Radiation What is the frequency of green light of wavelength 5200 Å?

Electromagnetic Radiation Max Planck - 1900 energy is quantized light has particle character Planck’s equation

Electromagnetic Radiation What is energy of a photon of green light with wavelength 5200 Å?

Electromagnetic Radiation What is energy of a photon of green light with wavelength 5200 Å?

Electromagnetic Radiation What is energy of a photon of green light with wavelength 5200 Å?

Atomic Spectra & Bohr Theory emission spectrum electric current passing through a gas in a vacuum tube (at very low pressure) causes the gas to emit light emission or bright line spectrum

Line Spectra Radiation composed of only one wavelength is monochromatic Radiation that spans an array of different wavelengths is continuous White light is continuous

Atomic Spectra & Bohr Theory absorption spectrum shining a beam of white light through a sample of gas gives an absorption spectrum shows the wavelengths of light that have been absorbed

Atomic Spectra & Bohr Theory spectra are fingerprints of elements use spectra to identify elements can even identify elements in stars

Atomic Spectra & Bohr Theory “how atoms talk to us” we have to interpret their language Bohr, Schrodinger, and Heisenberg were some of the first scientists to translate the language of atoms

Atomic Spectra & Bohr Theory An orange line of wavelength 5890 Å is observed in the emission spectrum of sodium. What is the energy of one photon of this orange light?

Atomic Spectra & Bohr Theory An orange line of wavelength 5890 Å is observed in the emission spectrum of sodium. What is the energy of one photon of this orange light?

Atomic Spectra & Bohr Theory Rydberg equation empirical equation that relates the wavelengths of the lines in the hydrogen spectrum (Equ. 6.4 text)

Atomic Spectra & Bohr Theory Neils Bohr - 1913 - incorporated Planck’s quantum theory into the H spectrum explanation Postulates of Bohr’s theory

Atomic Spectra & Bohr Theory Atom has a number of definite and discrete energy levels (orbits) in which an electron may exist without emitting or absorbing electromagnetic radiation. increasing radius of orbit increases the energy K<L<M<N<O......

Atomic Spectra & Bohr Theory An electron may move from one discrete energy level (orbit) to another and in doing so monochromatic radiation is emitted or absorbed in accordance with the following equation. E absorbed as electron jumps to higher orbit E emitted as electron falls to lower orbit

Atomic Spectra & Bohr Theory An electron moves in a circular orbit about the nucleus and its motion is governed by the ordinary laws of mechanics and electrostatics, with the restriction that the angular momentum of the electron is quantized (can only have certain discrete values). angular momentum = mvr = nh/2p h = Planck’s constant n = 1,2,3,4,...(energy levels) v = velocity of electron m = mass of electron r = radius of orbit

Atomic Spectra & Bohr Theory Bohr theory correctly explains H emission spectrum fails for all other elements just not an adequate theory

The Origin of Spectral Lines light of a characteristic wavelength (& frequency) is emitted when electron falls from higher E (orbit) to lower E (orbit) Origin of the emission spectrum light of a characteristic wavelength (& frequency) is absorbed when electron jumps from lower E (orbit) to higher E (orbit) origin of absorption spectrum

The Wave Nature of the Electron Louis de Broglie -1925 electrons have wave-like properties their wavelengths are described by the de Broglie relationship

The Wave Nature of the Electron verified by Davisson & Germer two years later electrons (in fact - all particles) have both a particle and a wave like character wave-particle duality is a fundamental property of submicroscopic particles

Quantum Mechanical Picture Werner Heisenberg - 1927 Uncertainty Principle It is impossible to determine simultaneously both the position & momentum of an electron.

Quantum Mechanical Picture devices for detecting motion of electron disturbs its position like measuring position of a car with a wrecking ball must speak of electrons in terms of probability functions

Quantum Numbers Basic Postulates of Quantum Theory Atoms and molecules can exist only in certain energy states. In each energy state, the atom or molecule has a definite energy. When an atom or molecule changes its energy state, it must emit or absorb just enough energy to bring it to the new energy state (the quantum condition).

Quantum Numbers Atoms or molecules emit or absorb radiation (light) as they change their energies. The frequency of the light emitted or absorbed is related to the energy change by a simple equation.

Quantum Numbers The allowed energy states of atoms and molecules can be described by sets of numbers called quantum numbers.

Quantum Numbers Quantum numbers are solutions of the Schrodinger, Heisenberg & Dirac equations electron wave functions Four quantum numbers are necessary to describe energy states of electrons in atoms

Quantum Numbers Principal quantum number - n n = 1, 2, 3, 4, ...... “shells” n = K, L, M, N, ...... electron’s energy depends principally on n

Quantum Numbers Subsidiary Quantum number - l l = 0, 1, 2, 3, 4, 5, .......(n-1) l = s, p, d, f, g, h, .......(n-1) tells us the shape of orbitals volume that the electrons occupy 90-95% of the time

Quantum Numbers Magnetic quantum number - ml l = 0, ml = 0 ml = - l, (- l + 1), (- l +2),.....0,.......,(l -2), (l -1), l l = 0, ml = 0 only 1 value s orbital l = 1, ml = -1,0,+1 3 values p orbitals

Quantum Numbers l = 2, ml = -2,-1,0,+1,+2 5 values d orbitals l = 3, ml = -3,-2,-1,0,+1,+2, +3 7 values f orbitals theoretically, we can continue this series on to g,h,i, orbitals

Quantum Numbers Spin Quantum Number - ms ms = +1/2 or -1/2 ms = ± 1/2 tells us the spin and orientation of the magnetic field of the electrons Wolfgang Pauli - 1925 Exclusion Principle No two electrons in an atom can have the same set of 4 quantum numbers.

Atomic Orbitals regions of space where the probability of finding an electron about an atom is highest described by either n (1,2,3,4,5,...) or letters (K,L,M,N,O,...) s orbitals spherically symmetric one s orbital per n level l = 0 1 value of ml

Atomic Orbitals s orbitals

Atomic Orbitals p orbitals start with n = 2 3 mutually perpendicular peanut shaped volumes directed along the axes of a Cartesian coordinate system 3 per n level, px, py, pz l = 1 ml = -1,0,+1 3 values of ml

Atomic Orbitals p orbitals

Atomic Orbitals d orbitals start with n = 3 4 clover leaf shaped and 1 peanut shaped with a doughnut around it on Cartesian axes and rotated 45o

Atomic Orbitals d orbitals start with n = 3 4 clover leaf shaped and 1 peanut shaped with a doughnut around it on Cartesian axes and rotated 45o 5 per n level l = 2 ml = -2,-1,0,+1,+2 5 values of ml

Atomic Orbitals d orbitals

Atomic Orbitals f orbitals most complex shaped orbitals start with n = 4 most complex shaped orbitals 7 per n level, complicated names l = 3 ml = -3,-2,-1,0,+1,+2, +3 7 values of ml important effects in lanthanides & actinides

Atomic Orbitals f orbitals

Atomic Orbitals spin effects every orbital can hold up to two electrons one spin up ­ one spin down ¯ spin describes the direction of their magnetic field unpaired electrons have their spins aligned ­­ or ¯¯

Atomic Orbitals paired electrons have spins unaligned ­¯ 2 electrons in same orbital must be paired consequence of Pauli Exclusion Principle

Atomic Orbitals number of orbitals per n level is given by n2 maximum number of electrons per n level is 2n2

Atomic Orbitals Energy Level # of Orbitals Max. # of e- n n2 2n2 1 1 2 1 1 2 2 4 8 3 9 18 4 16 32

Electronic Configurations Aufbau Principle - The electron that distinguishes an element from the previous element enters the lowest energy atomic orbital available.

Electronic Configurations

Electronic Configurations Aufbau Principle

Electronic Configurations use mnemonic

Electronic Configurations use periodic chart - best method

Electronic Configurations Write the electronic configuration for EVERY ATOM on the PERIODIC TABLE!!

Synthesis Question What is the atomic number of the element that should theoretically be the noble gas below Rn? The 6 d’s are completed with element 112 and the 7d’s are completed with element 118. Thus the next noble gas (or perhaps it will be a noble liquid) should be element 118.

Group Question In a universe different from ours, the laws of quantum mechanics are the same as ours with one small change. Electrons in this universe have three spin states, -1, 0, and +1, rather than the two, +1/2 and -1/2, that we have. What two elements in this universe would be the first and second noble gases? (Assume that the elements in this different universe have the same symbols as in ours.)