The Quantum Mechanical Atom Chapter 8

Electron Distribution When 2 or more atoms join to form a compound, the nuclei of the atoms stay relatively far apart. Only the atoms outer regions-the regions inhabited by electrons-come in close contact. Valence electrons (VE)-are the outermost electrons of an atom. They are involved in bonding events. The # of valence electrons (VE) for the representative elements groups 1A-8A can be predicted from the periodic table ***. Group # = VE# ***Note: He is in group 8A and has only 2 VE

Electron Configuration and Chemical Properties of Elements Elements within the same group have the same outer electron configuration (same # of VE), and thus similar chemical properties. The electronic structure of atoms has been elucidated based on studies regarding light which can be emitted or absorbed by an atom.

Electromagnetic Radiation Light is a form of energy that travels through space or matter by wavelike oscillations. Electromagnetic energy has an electric component and a magnetic component.

Maxwell (1873), proposed that visible light consists of electromagnetic waves. Electromagnetic radiation is the emission and transmission of energy in the form of electromagnetic waves. Speed of light (c) in vacuum = 3.00 x 10 8 m/s All electromagnetic radiation x  c

Properties of Waves Wavelength ( ) is the distance between identical points on successive waves. Amplitude is the vertical distance from the midline of a wave to the peak or trough.

Properties of Waves Frequency ( ) is the number of waves that pass through a particular point in 1 second (Hz = 1 cycle/s). The speed (u) of the wave = x

The Electromagnetic Spectrum Electromagnetic radiation comes from a broad range of frequencies called the electromagnetic spectrum. Only a small portion of the electromagnetic spectrum contains visible light with wavelengths nm.

Continuous Spectra

x = c = c/ = 3.00 x 10 8 m/s / 6.0 x 10 4 Hz = 5.0 x 10 3 m Radio wave A photon has a frequency of 6.0 x 10 4 Hz. Convert this frequency into wavelength (nm). Does this frequency fall in the visible region? = 5.0 x nm

Early 1900’s: Great Discoveries by Max Planck and Albert Einstein. Energy (light) is emitted or absorbed in discrete units (quantum). E = h x Planck’s constant (h) h = 6.63 x J s Light has both: 1.wave nature 2.particle nature Photon is a “particle” of light

E = h x E = 6.63 x (J s) x 3.00 x 10 8 (m/s) / x (m) E = 1.29 x J E = h x c /  When copper is bombarded with high-energy electrons, X rays are emitted. Calculate the energy (in joules) associated with the photons if the wavelength of the X rays is nm.

Atomic Spectra/Line Spectra Continuous spectra contains light of all colors (see previous slide) which is much different than an atomic spectra also called line spectra. Atomic spectra are observed when atoms are energized with a spark. Every element has its own unique atomic spectra which acts as a fingerprint for that element.

Line Emission Spectrum of Hydrogen Atoms

1.e - can only have specific (quantized) energy values. 2.light is emitted as e - moves from one energy level to a lower energy level. Bohr’s Model of the Atom (1913) Explains Atomic Spectra

Wave Properties of Matter and Wave Mechanics The classical laws of physics do not apply to particles as tiny as electrons. De Broglie (1924) reasoned that e - is both particle and wave. = h mv v = velocity of e- m = mass of e-

Quantum Mechanics How do we locate the exact location of a wave in space? How do we locate the exact location of a subatomic particle in an atom? Werner Heisenberg and Erwin Schrodinger attempt to solve these questions. 18

Heisenberg Uncertainty Principle It is impossible to know simultaneously both the momentum and the position of a particle with certainty in an atom. Applying this principle we see that in reality electrons do not orbit the nucleus of an atom in a well defined path as Bohr suggested. 19

20 Schrodinger Wave Equation In 1926 Schrodinger wrote an equation that described both the particle and wave nature of the e - Wave function (  psi ) describes: 1. energy of e - with a given  2. probability of finding e - in a volume of space Schrodinger’s equation can only be solved exactly for the hydrogen atom. Must approximate its solution for multi-electron systems.

Schrodinger Equation The probability of finding an electron in 3D space around the nucleus of an atom is proportional to the square of the wave function. (  ) ^2 = ( n, l, m l, m s ) 21

Quantum Mechanics Results in our understanding that electrons in atoms exist in certain energy levels around the nucleus called shells. Shells are numbered 1,2,3 etc with number 1 being the lowest in energy and closest to the nucleus. The number of electrons in any particular shell is limited by the equation: Maximum # of electrons per shell= 2n 2 n=1,2,3,4…

Quantum Mechanics Each shell consists of subshells. A subshell is a sub-energy level labeled s,p,d,f. Subshells are composed of orbitals. The number of orbitals per subshell and the maximum number of electrons that can exist within them are described on page 328.

Electron Orbitals Regions in space around a nucleus where there is a high probability of finding electrons. Each region has a distinct shape. 24

25 s orbitals p orbitals

26 d orbitals

27 Schrodinger Wave Equation In 1926 Schrodinger wrote an equation that described both the particle and wave nature of the e - Wave function (  ) describes: 1. energy of e - with a given  2. probability of finding e - in a volume of space Schrodinger’s equation can only be solved exactly for the hydrogen atom. Must approximate its solution for multi-electron systems.

28 Schrodinger Wave Equation  is a function of four numbers called quantum numbers (n, l, m l, m s ) principal quantum number n n = 1, 2, 3, 4, …. n=1 n=2 n=3 distance of e - from the nucleus

29 quantum numbers: (n, l, m l, m s ) angular momentum quantum number l for a given value of n, l = 0, 1, 2, 3, … n-1 n = 1, l = 0 n = 2, l = 0 or 1 n = 3, l = 0, 1, or 2 Shape of the “volume” of space that the e - occupies l = 0 s orbital l = 1 p orbital l = 2 d orbital l = 3 f orbital Schrodinger Wave Equation

30 l = 0 (s orbitals) l = 1 (p orbitals)

31 l = 2 (d orbitals)

32 quantum numbers: (n, l, m l, m s ) magnetic quantum number m l for a given value of l m l = -l, …., 0, …. +l orientation of the orbital in space if l = 1 (p orbital), m l = -1, 0, or 1 if l = 2 (d orbital), m l = -2, -1, 0, 1, or 2 Schrodinger Wave Equation

33 m l = -1, 0, or 1 3 orientations is space

34 m l = -2, -1, 0, 1, or 25 orientations is space

35 (n, l, m l, m s ) spin quantum number m s m s = +½ or -½ Schrodinger Wave Equation m s = -½m s = +½

36 Existence (and energy) of electron in atom is described by its unique wave function . Pauli exclusion principle - no two electrons in an atom can have the same four quantum numbers. Schrodinger Wave Equation quantum numbers: (n, l, m l, m s ) Each seat is uniquely identified (E, R12, S8) Each seat can hold only one individual at a time

37 Schrodinger Wave Equation quantum numbers: (n, l, m l, m s ) Shell – electrons with the same value of n Subshell – electrons with the same values of n and l Orbital – electrons with the same values of n, l, and m l How many electrons can an orbital hold? If n, l, and m l are fixed, then m s = ½ or - ½  = (n, l, m l, ½ ) or  = (n, l, m l, - ½ ) An orbital can hold 2 electrons

38 How many 2p orbitals are there in an atom? 2p2p n=2 l = 1 If l = 1, then m l = -1, 0, or +1 3 orbitals How many electrons can be placed in the 3d subshell? 3d3d n=3 l = 2 If l = 2, then m l = -2, -1, 0, +1, or +2 5 orbitals which can hold a total of 10 e -

Energy of orbitals in a single electron atom n=1 n=2 n=3

Energy of orbitals in a multi-electron atom n=1 n=2 n=3

Filling of Subshells and the Electron Energy Diagram An atom is in its most stable state when its electrons are at the lowest possible energies. Filling of an electron energy diagram must be done from the bottom (n=1) then upward. When placing electrons in their respective orbitals one must take into consideration the Aufbau principle, the Pauli Exlusion Principle, and Hunds Rule.

“Fill up” electrons in lowest energy orbitals (Aufbau principle) H 1 electron H 1s 1 He 2 electrons He 1s 2 Li 3 electrons Li 1s 2 2s 1 Be 4 electrons Be 1s 2 2s 2 B 5 electrons B 1s 2 2s 2 2p 1 C 6 electrons ??

Pauli exclusion principle - no two electrons can have the same spin when they are both in the same orbital.

C 6 electrons The most stable arrangement of electrons in subshells is the one with the greatest number of parallel spins (Hund’s rule). C 1s 2 2s 2 2p 2 N 7 electrons N 1s 2 2s 2 2p 3 O 8 electrons O 1s 2 2s 2 2p 4 F 9 electrons F 1s 2 2s 2 2p 5 Ne 10 electrons Ne 1s 2 2s 2 2p 6

Order of orbitals (filling) in multi-electron atom 1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s

Electron configuration is how the electrons are distributed among the various atomic orbitals in an atom. 1s 1 Shell number n orbital number of electrons in the orbital or subshell Orbital diagram H 1s 1

Shells, Subshells, and Orbitals

What is the electron configuration of Mg? Mg 12 electrons 1s < 2s < 2p < 3s < 3p < 4s 1s 2 2s 2 2p 6 3s = 12 electrons Abbreviated as [Ne]3s 2 [Ne] 1s 2 2s 2 2p 6 What is electron configuration of Cl? Cl 17 electrons1s < 2s < 2p < 3s < 3p < 4s 1s 2 2s 2 2p 6 3s 2 3p = 17 electrons Last electron added to 3p orbital

Paramagnetic unpaired electrons 2p Diamagnetic all electrons paired 2p 7.8 Paramagnetic substances are attracted to a magnetic field

THE END