Atoms Where are the electrons? RPI - ERTH 2330
Louis Victor de Broglie (1925) said that the wavelength of any particle of mass ( m ) and velocity v is � = h/ mv h is equal to 6.6262 E -34 Js.
Electrons as waves… E.B. Watson the wavelength of any particle � = h / mv
Standing Waves
A free electron moves in a traveling wave, like a ripple across the water. When it becomes captured by an atom, its movement is that of a standing wave. n = 1 n = 2 n = 3 n = 4 E.B. Watson
A variable that is allowed by the system to have only certain discrete values is said to be quantized . The variable n , which enumerates these permitted values is called a quantum number .
Uncertainty Heisenberg uncertainty principle Problem – we cannot measure the position and velocity of a small particle at the same time. E.B. Watson
Remember � = 2L/n? (2D wave – guitar string) Meet � (3D wave) Integers n, l , m Describe r, � , and � Quantization E.B. Watson Principle ( n ) distance 1, 2, 3, 4,… Angular mo. ( l ) shape 0 to n – 1, 0 is spherical Magnetic ( m ) orientation - l to + l
orientation distance sphericity Wave function We are forced to describe the position of the electron in terms of probability � 2 n, l, m The electron around a nucleus is highly likely to be in a quantized standing wave .
E.B. Watson
s orbital E.B. Watson
E.B. Watson
p orbital E.B. Watson
n > 2 l = 1 m = -1 , 0 , 1
d orbital for n > 2, l = 2 m = -2, -1, 0, 1, 2 balloons extending from nucleus at right angles
f orbital for n > 3, l = 3 m = -3, -2, -1, 0, 1, 2, 3 Geometry is very complex Image from Kotz and Purcell, 1987
Hydrogen (H) Energy for position for one electron In other words, the electron could be in any one of these � E = 10.25 eV circles - but only as a function of available energy BTW – an eV is an electron volt and is 1.60217646 E -19 Joules
Energy and electron position. •lowest 1s orbital - ground state for hydrogen. •2s and 2p are same energy, greater than that of the 1s, and are energetically equivalent (for hydrogen). •there is a direct relationship between orbital size and energy level. •Increasing n means decreasing � E.
So – a single electron’s position may be defined by its probability to be in a certain orbital (s, p, d, or f), as defined by � 2 n, l , m . It’s position caries a certain energy. Beyond Hydrogen: Multiple electron atoms The wave function must define only one electron. Two unidentical electrons may occupy one orbital. We need one more number in our wave function!!
We have three n, l, m . However, we may place two electrons in each wave number (orbital). Introducing s , the term for the spin of the electron Two values +1/2 and -1/2. Terms carry a direction component (pos or neg) and a symmetry component (1/2). The spin is related to the angular momentum of the electron.
Electrons are spinning particles, and they may spin in one orbital in either positive or negative directions. But they may not spin in the same direction within one orbital – thus, n, m, l, s combine to describe a unique place for an electron (Pauli Exclusion Principle)
Table of electron wave functions Note: the orbital letter is determined by the value of l .
Remember Any single object with mass and velocity can be defined as a wave The uncertainty of observing the mass requires a probability treatment Nick Kim’s cartoon pokes fun at getting carried away with this…
Ground State The lowest amount of energy used to retain the electrons is called a ground state. On the graph on the right, what are the two possible ground states for a hydrogen atom?
Hund’s rule: electrons retain parallel spin as much as possible. We end up with this : 2 p x 2 p y 2 p z � � 1s 2s 2p not this: B 2 p x 2 p y 2 p z C �� N O
Predicting the arrangement of atoms He- 2 electrons - both share the 1s orbital Li - 3 electrons - two share 1s, and one in 2s There is an increased nuclear charge with greater Z. Therefore, spatial equivalency doesn’t mean equivalent energies!
4s is lower than 3d!
Notation:
Notation:
Size of Atom Decrease across a period. Increase down a group When moving across a period of main group elements, the size decreases because the effective nuclear charge increases.
For more than one electron: Electrostatic repulsion between electrons Increased nuclear charge (larger # of protons)
Stripping off an electron A certain quantity of energy is needed to evict an electron from its home.
Ionization Energies
Mendeleev’s Table Image from Kotz and Purcell, 1987
E.B. Watson
Electron configuration and periodicity
For more than one electron: Electrostatic repulsion between electrons Increased nuclear charge (larger # of protons)
f d
The periodic table Elements 1 through 20 easily divide the behavior into 8 periods based on the numbers of electrons in the highest energy orbital
Group 3b-2b - The transition elements Beyond 20 - the d orbital; room for 10 electrons with no or little change in energy. However, the d orbital can split energies (2 up, 3 down or inverse) if needed. Transition state
Lanthanides and Actinides The f orbital - naturally occurring lanthanides are known as the Rare Earth Elements (REE’s). 6s provides valence (+2; except divalent Eu)
Valence The number of bonds that an atom can form as part of a compound is expressed by the valence of the element. Goal -atoms want to end up in compounds that give them a noble-gas-like configuration. • Singles (like Na) form only one bond, and are therefore monovalent • Magnesium has a valency of two (divalent) For elements on the right side of the periodic table and sub 20 III-V elements, valence is the number of outermost electrons.
Group VI-VII elements require additional electrons, as they have nearly complete valence shells. Their valence is determined by what they lack (O is divalent). Transition elements may have multiple valences. Fe is best example. So do may heavy elements in p-block - these depend on what and how they are bonded.
Notation We may denote how many electrons are present in a neutral ground-state atom a number of different ways. One presentation - dots surrounding the atomic symbol - Lewis Structures Potassium has 19 electrons K [Ar] 4s 1 Sulfur has 16, [Ne] 2s 2 2p 4 - Four S electrons in p, two in s Strontium has 38 Sr [Kr] 5s 2
Ions are atoms that carry a charge as valence electrons are lost/gained Cation - Atom loses electron(s) (becomes positive) [Ca] 2+ Calcium Ca 2+ Anions - Atom gains electron(s) (becomes negative) [ O ] 2- Oxygen O 2-
Ionization Valence electrons are those easiest to move from their low- energy orbital away from the attraction of the Atom. As such, its relatively cheap to move the electron(s) out of the s-orbital or into the p-orbital Column IA (1) has 1 valence electron - ions may be created by removing the s orbital electron Column IIA (2) has 2 valence electrons at the same ionization energy, ions may be removing both electrons from the s orbital. Column VIA (15) lacks two electrons to complete the p-orbital. Column VIIA (16) lacks one electron to complete the p-orbital
Group IA, 1 valence electron (p 1 ), form +1 cation Group IIA, 2 valence electrons (p 2 ), form +2 cations Group VIA, 6 valence electrons (p 2 d 4 ), form -2 anions Group VIIA, 7 valence electrons (p 2 d 5 ), form -1 anions
Okay, why does this work? Low � E between electron configurations This works when one considers the shape of the orbitals as they interact with those of adjacent atoms (oxygen)
Ionization occurs either by losing or gaining electrons Linus Pauling quantified the ability of an atom to attract (gain) electrons. He termed this quantity electronegativity.
Electronegativity capacity of an atom to attract extra electrons Image from Gill, 1996
How big is an ion? Ionic Radius - the size A cation is always smaller than the atom from which it is derived (because it has lost an electron) Example: Li 1.52 Å Li + 0.82 Å An anion is always bigger than the atom from which it is derived. Example: F 0.64 Å F - 1.25 Å Ionic radii are not fixed - they depend on the degree of ionization and any adjacent atoms to which they are bonded.
Similar Behavior Image modified from Gill, 1996
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