Chapter 4:  ARRANGEMENT OF ELECTRONS IN ATOMS

Electromagnetic Spectrum, Energy and the  Electron

A.  Planck – energy is quantized:  is not continuous,  energy can only be gained or released in discrete units,  each unit is called a quantum, plural is quanta, energy has properties of particulate matter

B.  Albert Einstein – German-born American physicist,  Published three papers in 1905 1)photoelectric effect :  photons, having a minimum amount of energy, striking the surface of a metal can cause electrons to be ejected from the surface, varying the intensity of light striking the surface can directly change the number of electrons leaving the surface and varying the frequency (energy) of light striking the surface can directly change the energy of the electrons leaving the surface,  electromagnetic radiation is a stream of particles called photons;  2)special relativity:  E = mc2  (energy has mass);  3)Brownian motion

From Planck and Einstein - the dual nature of light and matter

C.  Bohr – founder of modern physics,   must be in orbits of a specific energy – they can absorb energy to move to higher level creating an excited state – they can give off energy as light and move back to the original ground state – E = hn

D.  de Broglie – matter and radiation have both wave and particulate properties – l = h/mc

E.  Heisenberg – founder of the modern quantum theory and Heisenberg's Uncertainty Principle:  There is a limit to being able to know the exact position and momentum of an electron accurately.

F.  Schrodinger – mathematical equations used to wave function, the solution describes the orbital of electron by a set of three quantum numbers ( n, l, and ml)

G.  Stern – described the magnetic properties of atoms,  fourth quantum number, ms

H.  Pauli – modern quantum mechanics and Pauli’s Exclusion Principle: In an atom, no two electrons can have the same set of four quantum numbers.  Since an orbital can hold two electrons, the first three quantum numbers will be the same.  The principle means the last quantum number must be different, the electrons in the same orbital must spin in oppositedirections.

I.  Aufbau principle:  as protons are added to the nucleus for each successive element, electrons are added to hydrogenlike orbitals, lowest energies filled first. 

J.  Hund's rule:  single electrons in degenerate orbitals have the same spin.  This is the lowest energy configuration for an atom, the one with the most unpaired electrons possible by the Pauli principle.

 

                If matter can behave like a wave, it must have wave properties.  Amplitude is the height, or maximum displacement from zero, of the wave.  Wavelength (lambda: l)  is the distance between two consecutuve peaks or troughs in a wave.  Frequency (nu: n) is the number of waves (cycles) per second that pass a given point in space.  Hertz measures frequency, it is 1/sec or sec-1.  The energy of a wave is directly related to it's frequency, E = hn.  Wavelength and frequency are inversely related, l . n = c (c is the speed of light in a vacuum, 3.0 x 108 m/s). 

                Bohr reasoned that the orbits of the electrons surrounding the nucleus must have a definite diameter.  He determined that an electron could emit energy of one or two quanta, but not 1.5 or 3.2 quanta, as it fell to a lower energy level.

                A ball bouncing from one step to another represents the motion of an electron as it falls from one energy level to another.  Each step is a different energy level.  The bottom of the staircase represents the the lowest energy level within an atom.  This is called the ground state or the S state.  It is the smallest orbit  of an electron.  To reach a higher step, energy must be absorbed.  A higher step is called the excited state or P state.

                The spectra produced by a compound can be used to determine the elements in a compound.  Each line of the spectrum represents one frequency of light, and therefore a certain energy (E = hn).  This energy is determined by the movement of electrons between energy levels which are specific for each element.  The same set of energy levels will always produce the same spectrum.  When an electron falls from a higher to a lower energy level, a photon is emitted.  As an electron moves farther from the nucleus, it absorbs energy.

 

Electron Configurations

Electrons are found at specific energy levels in the electron cloud surrounding the nucleus.

1)   Each level can hold up to a maximum number of electrons.  This amount is given by the expression 2(n2), where n is the principle energy level. 

2)  a.  Each level is split into sublevels.  There can be the same number of sublevels as the level number. 

     b.  The sublevels within each level have different amounts of energy.  The one with the lowest energy is called the s  sublevel.  The other sublevels in order of increasing energies are p, d, and f.  So  s  < p  < d  < f.   (The letters stand for the words used to represent the X-ray spectrum lines split;  s - sharp, p - principle, d - diffuse and f - fundamental.)

     c.  Level 1 has only 1 sublevel and can have a maximum of 2 electrons.  The lowest sublevel on every level is an s.  Therefore the s  sublevel on level 1 must contain these 2 electrons (and every s  sublevel can hold a maximum of 2 electrons).  Level 2 can hold 8 electrons and has 2 sublevels than the lowest sublevel is an s  and the other is a p.  The s  sublevel can hold a maximum of 2 electrons so the p  sublevel must hold the remaining 6 electrons.  In a likewise manner, level 3 has an s, a p  and a d,  with d  holding a maximum of 10 electrons;  level 4 has an s, a p, a d, and an f , with f  holding a maximum of 14 electrons.

3)  Each sublevel is split into orbitals.  Each orbital can hold a maximum of 2 electrons.  Since the s  sublevel has a maximum of 2 electrons they must be in the same orbital.  Therefore an s  sublevel has 1 orbital.  The p  sublevel has 6 electrons and if they are paired, then the p  sublevel has 3 orbitals.  The d  sublevel has 10 electrons and if they are paired, then the d  sublevel has 5 orbitals.  The f  sublevel has 14 electrons and if they are paired, then the f  sublevel has 7 orbitals.

4)  The 2 electrons in each orbital both have negative charges and will repel each other.  To be able to occupy the same orbital and reduce the repulsion forces, the electrons must spin in opposite directions.  One electron will spin in a clockwise direction and the other will spin in the counterclockwise direction.

5)  Electrons fill these levels (and sublevels and orbitals) in a concise manner:  based on the Aufbrau Principle and Hund's Rule, the electron configuration which has the lowest energy is filled first. 

6)  However -  the sublevels of the higher levels start overlapping the sublevels of some of the lower levels.   In order of increasing energies electrons fill in the following manner: 

                                1s  2s  2p  3s  3p  4s  3d  4p  5s  4d  5p  6s  4f  5d  6p  7s  5f  6d  7p  8s.

7)                   A superscript denotes how many electrons are on that sublevel.  If you add the superscripts it will also tell you the total number of electrons, and for a neutral atom this is the atomic number of the element.

8)       The diagonal rule can be used to predict the electron configuration for

the ground state of an atom.  Start at the top right and follow the arrow

along the diagonal to the bottom left.  At the end of the arrow, go to the

top of the next diagonal and repeat until enough electrons have been used.

 

Summary of Electron Configurations

1)  Levels                            # e- [2(n)2]                     # Sublevels         

                1                              2                                              1 - s                        

                2                              8                                              2 - s, p                    

                3                              18                                            3 - s, p, d               

                4                              32                                            4 - s, p, d, f          

2)  Sublevel                       # e-                                           # Orbitals       

                s                              2                                                              1             

                p                              6                                                              3             

                d                              10                                                            5             

                f                               14                                                            7             

 

Orbital Filling Diagram

1)  Electrons on the highest energy level only, unless a d  or an f  sublevel is partially filled, then that sublevel must be shown.

2)  Always an s  and a p  sublevel  (although they may not be filled), and a d

3)  s  has 1 orbital, p  has 3 orbitals, d  has 5 orbitals, and f  has 7 orbitals

4)  Each orbital can hold a maximum of 2 electron, one spinning clockwise ( | ) and the other spinning counterclockwise ( | )

5)  Least energy fills first, therefore s  will fill with 2 electrons before p  has any

6)  The first electron in an orbital will spin clockwise, the second will spin counterclockwise.

7)  Each p  orbital has one clockwise spinning electron before any has a second counterclockwise spinning electron.  d  and f  fill in this same manner.

               

Quantum Numbers - a set of four numbers used to describe the probability of finding an electron in any one place in the electron cloud.

1)  First quantum number is n, the principle quantum number, the energy level.  It represents the distance from the nucleus or the size of the electron cloud.     values for n:  any non-zero, positive whole number;  therefore n = 1, 2, 3,    etc

2)  Second quantum number is l, the sublevel.  It represents the shape of the electron cloud.     values for l:  any non-negative whole number from zero to on less than n;    therefore l =0, 1, ...n -1, which means s  = 0, p = 1, d  = 2  and f  = 3

3)  Third quantum number is m, the orbital.  It represents the direction in space of the electron cloud.     values for m:  whole numbers from a negative to a positive l, therefore m = -l...0...+l

4)  Fourth quantum number is s, the spin of the electron.  This is either in a clockwise or a counter clockwise direction.   values:  s = +1/2   OR  s = -1/2

 

Summary of Quantum Numbers

                n                              l                                               m                                                             s                             

                1                              0                                              0                                              +1/2    OR    -1/2               

                2                              0                                              0                                              +1/2    OR    -1/2

                                                1                                           -1, 0, +1                                            +1/2    OR    -1/2               

                3                              0                                              0                                              +1/2    OR    -1/2

                                                1                                     -1, 0, +1                                            +1/2    OR    -1/2

                                                2                                -2, -1, 0, +1, +2                     +1/2    OR    -1/2               

                4                              0                                              0                                              +1/2    OR    -1/2

                                                1                                     -1, 0, +1                                            +1/2    OR    -1/2

                                                2                                -2, -1, 0, +1, +2                     +1/2    OR    -1/2

                                                3                         3, -2, -1, 0, +1, +2, +3                            +1/2    OR    -1/2