ATOMIC ORBITALS

The Quantum Model of an Atom and Electron Configuration

THE QUANTUM CONCEPT   In 1900, Max Planck proposed the controversial idea that energy was emitted in small bundles (quanta), not continuously.   → proposal that light is also emitted in small bundles called photons

Photon  Photon is the elementary particle responsible for electromagnetic phenomena.  It is the carrier of electromagnetic radiation of all wavelengths, including gamma rays, X-rays, ultraviolet light, visible light, infrared light, microwaves, and radio waves.

BOHR MODEL OF THE ATOM   In 1913, Neils Bohr speculated that in the atom, electrons revolve around the nucleus, occupying circular orbits with distinct energy levels.

ENERGY LEVELS AND SUBLEVELS n = 1, K n = 2, L n = 3, M n = 4, N For elements (w/ more than 1 proton and more than 1 electron), principal energy level, n (numbered 1, 2, 3,…) are further divided into energy sublevels. principal energy level (n): n=1,2,3,... energy sublevels: s, p, d, and f

ENERGY LEVELS AND SUBLEVELS

QUANTUM MECHANICAL MODEL OF THE ATOM

Shapes of Orbitals   – S orbitals are spherical   – As principal number ↑, the size and energy of the orbitals ↑

Shapes of Orbitals   P orbitals resemble dumbbells, lying along the x,y, and z axes   – Putting all three p orbitals together results in an orbital set that is close to spherical in shape

Shapes of Orbitals   The five d orbitals have two different shapes:   –4 are clover leaf shaped.   –1 is peanut shaped with a doughnut around it.   –The orbitals lie directly on the Cartesian axes or are rotated 45 o

Shapes of Orbitals  The seven f orbitals

Shapes of Orbitals  The nine g orbitals

K Shell 2 electrons Nucleus 11 protons 12 neutrons L Shell 8 electrons M Shell 1 electron Bohr Representations of 11Na Atom

O ccupancy of the E nergy L evels  Minimum = 1 e-  Maximum = 2n 2 K n = 12n 2 = 2 Ln = 2 2n 2 = 8 Mn = 3 2n 2 = 18 Nn = 4 2n 2 = 32

ACTIVITY Draw the Bohr structure of the elements from atomic numbers 2 to 20.

P + = 2 n 0 = 2 n 0 = 2 2 He 4 2e - K 3 Li 7 P + = 3 n 0 = 4 n 0 = 4 2e - K 1e - L 4 Be 9 P + = 4 n 0 = 5 n 0 = 5 2e - K L 5 B 10 P + = 5 n 0 = 5 n 0 = 5 2e - K 3e - L 6 C 12 P + = 6 n 0 = 6 n 0 = 6 2e - K 4e - L 7 N 14 P + = 7 n 0 = 7 n 0 = 7 2e - K 5e - L

8 O 16 P + = 8 n 0 = 8 n 0 = 8 2e - K 6e - L 9 F 19 P + = 9 n 0 = 10 n 0 = 10 2e - K 7e - L 10 Ne 20 P + =10 n 0 = 10 n 0 = 10 2e - K 8e - L 11 Na 23 12Mg24 13 Al 27 P + =11 n 0 = 12 n 0 = 12 2e - K 8e - L 1e - M P+ =12 n0 = 12 2e- K 2e - K 8e - L 8e- L 3e - M 2e- M P + =13 n 0 = 14 n 0 = 14

14 Si P S Cl 35 6e - M P + =14 n 0 = 15 n 0 = 15 P + =15 n 0 = 15 n 0 = 15 P + =16 n 0 = 16 n 0 = 16 P + =17 n 0 = 18 n 0 = 18 2e - K K K K 8e - L L L L 4e - M 5e - M 7e - M

19 K Ca 40 P + =20 n 0 = 20 n 0 = 20 P + =19 n 0 = 20 n 0 = 20 2e - K K 8e - L L 9e - M 10e - M 18 Ar 40 P + =18 n 0 = 20 n 0 = 20 2e - K 8e - L M

O ctet R ule – also known as the Rule of Eight 19 K 2e - 8e - 9e - KLM 19 K 2e - 8e - 8e - 1e - KLMN

20 Ca 2e - 8e - 10e - KLM 20 Ca 2e - 8e - 8e - 2e - KLMN

ELECTRON CONFIGURATION   1. Electrons are distributed in orbitals of increasing energy levels, where the lowest energy orbitals are filled first.   2. Once an orbital has the maximum number of electrons it can hold, it is considered “filled.” Remaining electrons must then be placed into the next highest energy orbital, and so on.   Orbitals in order of increasing energy:   1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s < 5d < 6p

ELECTRON CONFIGURATION   – Shorthand description of the arrangement of electrons by sublevel according   to increasing energy   REMEMBER!   — s orbitals can hold 2 electrons   — a set of p orbitals can hold 6 electrons   — a set of d orbitals can hold 10 electrons   — a set of f orbitals can hold 14 electrons

A ufbau “ B uilding- U p” P rinciple  Electrons enter into orbital in the order of increasing energy until the proper number of electrons of an element has been accommodated  The Aufbau principle from German "Aufbau" meaning "buildup" (also Aufbau rule or building-up principle), is used to determine the electron configuration of an atom, molecule or ion..

A ufbau “ B uilding- U p“ P rinciple 1s2s3s4s5s6s7s 2p3p4p5p6p7p 3d4d5d6d7d 4f5f6f7f

Frederick Hund Hund’s Rule of Maximum Multiplicity... applies to degenerate orbitals (also called the Rule of Half-filling)

7 N 1s 2 2s 2 2p x 1 2p y 1 2p z 1 6 C 1s 2 2s 2 2p x 1 2p y 1 No pairing of electrons is possible unless all orbitals in the same subshell have one electron each. Do the EC of elements with atomic numbers 8 to 15 Hund’s Rule of Maximum Multiplicity

8 O 1s 2 2s 2 2p x 2 2p y 1 2p z 1 9 F 1s 2 2s 2 2p x 2 2p y 2 2p z 1 10 Ne 1s 2 2s 2 2p x 2 2p y 2 2p z 2 11 Na 1s 2 2s 2 2p x 2 2p y 2 2p z 2 2s 1 12 Mg 1s 2 2s 2 2p x 2 2p y 2 2p z 2 3s 2 13 Al 1s 2 2s 2 2p x 2 2p y 2 2p z 2 3s 2 3p x 1 14 Si 1s 2 2s 2 2p x 2 2p y 2 2p z 2 3s 2 3p x 1 3 p y 1 15 P 1s 2 2s 2 2p x 2 2p y 2 2p z 2 3s 2 3p x 1 3p y 1 3p z 1 Hund’s Rule of Maximum Multiplicity

Activity: EC  1. Ca  2. Fr  3. Sr  4. Mo  5. Pb  6. As  7. Ni  8. I  Ca = 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2  Fr = 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 4p 6 5s 2 4d 10 5p 6 6s 2 4f 14 5d 10 6p 6 7s 1  Sr = 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 4p 6 5s 2  Mo = 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 4p 6 5s 2 4d 4  Pb = 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 4p 6 5s 2 4d 10 5p 6 6s 2 4f 14 5d 10 6p 2 4d 10 5p 6 6s 2 4f 14 5d 10 6p 2  As = 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 4p 3  Ni = 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 8  I = 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 4p 6 5s 2 4d 10 5p 5 4d 10 5p 5

The Quantum Theory

Louis de Broglie 1924 LOUIS DE BROGLIE (French) combined equations from Einstein and Planck to show that electrons have specific wavelengths and wave-like properties.

(Austrian) described the motion of electrons in atoms by a mathematical equation that combined the particle nature of an electron, wave properties, and quantum restrictions, in a probability relationship ERWIN SCHROEDINGER Erwin Schroedinger

1927 Werner Heisenberg   developed the concept of the Uncertainty Principle.   It is impossible to determine simultaneously both the position and momentum (mv) of an electron (or any other small particle).   We define electron energy exactly but accept W. Heisenberg

The Quantum Numbers   Quantum numbers are the solutions of the Schrodinger, Heisenberg & Dirac equations.   We use quantum numbers to designate the electronic arrangements in all atoms.   Four quantum numbers (n, l, m, s) are necessary to describe energy states of electrons in atoms. Paul Dirac

A.SCHROEDINGER 's equation is based on the four quantum numbers: n, l, m, s n = period, principle energy level l = s, p, d, f orbital type, sublevel m = orientation of orbitals (angular momentum) s = spin The Quantum Numbers

  The principal quantum number has the symbol – n.   n = 1, 2, 3, 4, “shells”   n = K, L, M, N,   The electron’s energy depends principally on n. Value of n is the main factor (but not the only one) that determines the energy of an electron and its distance from the nucleus. Maximum capacity for energy level = 2n 2 Principle Energy Level

Sublevels   The angular momentum quantum number has the symbol l.   l = 0, 1, 2, 3, 4, 5, (n-1)   l tells us the shape of the orbitals. n = 1l = 0 (One sublevel) n = 2l = 0, 1 (Two sublevels) n = 3l = 0, 1, 2 (Three sublevels) n = 4l = 0, 1, 2, 3 (Four sublevels)

Sublevels   electrons for which   These orbitals are the volume around the atom that the electrons occupy 90-95% of the time. l = 0 are called s(Stands for sharp) spherical l = 1 are called p(Stands for principle) perpendicular l = 2 are called d(Stands for diffuse) l = 3 are called f(Stands for fundamental)

  The symbol for the magnetic quantum number is m.   m = -l, (-l + 1), (-l+2),.....0, , (l-2), (l-1),   If l = 0 (or an s orbital), then m = 0.   –Notice that there is only 1 value of m.   This implies that there is one s orbital per n value. n ≥1   If l = 1 (or a p orbital), then m= -1,0,+1.   There are 3 values of m.   Thus there are three p orbitals per n value. n ≥2 Orbitals

Orbitals  Each sublevel contains one or more orbitals.  m describes the orientation of the electron cloud.  For any value of l, m may have any integral values between -l and l.  i.e. l = 2 ml = -2, -1, 0, 1, 2 (5 oribtals)  For any l there are 2l + 1 orbitals in that sublevel.

  If l = 2 (or a d orbital), then m = -2,-1,0,+1,+2.   –There are 5 values of m.   Thus there are five d orbitals per n value. n ≥3   If l = 3 (or an f orbital), then m= -3,-2,-1,0,+1,+2, +3.   –There are 7 values of m.   Thus there are seven f orbitals per n value, n The Quantum Numbers - m

  The last quantum number is the spin quantum number which has the symbol s.   The spin quantum number only has two possible values.   –s = +1/2 or -1/2   This quantum number tells us the spin and orientation of the magnetic field of the electrons. Only two (2) electrons with opposite spins are allowed per orbital. The Quantum Numbers - s

Spin s = spin an electron. Can have one of 2 spins +, and -. Electrons that have the same value of ms are said to have parallel spins. Electrons that have different ms values are said to have opposed spins. For 2 electrons to exist in thee same orbital, they must have opposed spins.

P auli`s E xclusion P rinciple Wolfgang Pauli in 1925 discovered the Exclusion Principle. No two (2) electrons in the same atom may have identical set of all four (4) quantum numbers. Wolfgang Pauli

S pins of E lectrons same orbital different orbitals

Total Energy of an e - = (n+l) nl n + l 4s 3d

Example: 3p 4 Example: 3p 4  n = main energy level  l = shape orbital  = 0 for s, 1 for p 2 for d, 3 for f 2 for d, 3 for f  m = s  = p  = d  = f  s = -1/2 or +1/2 if unpaired or paired electrons occupy an orbital  n = 3  l = 1, since it’s a p orbital a p orbital  m = -1  s = +1/

Q UANTUM N UMBERS shellnshelllsubshellnorbitalsspin Total e - per subshell K L M N p s s s s p p d d f /+ 12 -/+ 1/

A DDRESSES OF F IRST T EN E LECTRONS IN A TOMS L s s p s s m n l K s pxpxpxpx pypypypy pzpzpzpz 2nd1st1st1st1st1st2nd2nd2nd2nd /2+1/2-1/2-1/2-1/2-1/2+1/2+1/2+1/2+1/2 shorthand 1s 1 1s 2 2s 1 2s 2 2p x 1 2p x 2 2p y 1 2p z 1 2p z 2 2p y 2

Activity Give the Set of Quantum Numbers of the Following Elements and Identify the Atomic Number  4s 2  3p 2  7s 1  4d 8  5f 6  6p 6  5d 4  2p 3

Activity Given the Set of Quantum Numbers Identify the Elements n436 l210 m+20 s-1/2+1/2-1/ /2-1/2+1/2-1/2

Summary  Pauli Exclusion Principle: No two electrons in the same atom can have the same set of quantum numbers.  Procedure for placing electrons in an atom: Aufbau Principle: Electrons are added to sublevels in the order of increasing energy. Generally fills each sublevel before beginning the next.  Hund's Rule: When filling orbitals of equal energy (degenerate orbitals) order is such that as many electrons as possible remain unpaired.

Summary

 End of presentation  Exam Next Meeting