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The Electron Part 2 The Quantum Model of the Atom • In 1927, Werner Heisenberg proposed his uncertainty principle. – You can’t know both the velocity & position of a particle at the same time – Meaning we can’t predict the exact location of an e- or it’s path in the atom – Whatever you use to measure the location of an electron will cause the electron to move To detect the position of an electron you might use a photon. Unfortunately, when the photon collides with the electron the force of the collision causes the electron to change position, so the best you can tell is where the electron was. The Quantum Model of the Atom • The biggest effect of the Uncertainty Principle on Bohr’s model is that there is no way to define the path of the e- around its nucleus with any accuracy. – The best we can do is make an educ- ated guess within a certain range of probability that the e- is in a particular region around the nucleus. The Quantum Model of the Atom • In 1926, the physicist Erwin Schrod- inger took the atom 1 step further. – He proposed a mathematical equation to describe the location & energy of the e- in a H atom. – He used calculated the “wave func- tion” of the e-, or the probability of locating the e- a certain distance from the nucleus • the quantum mechanical model is based on Schrodinger’s work. The Quantum Model of the Atom The Quantum Model of the Atom • Like the Bohr model, the quantum mech model of the atom restricts the energy of e-’s to quantized values. – But, the quantum mechanical model doesn’t define a specific path an elec- tron takes around the nucleus. • Instead it estimates the probability of finding an electron in a certain position. Bohr’s model gave the e- specific paths around the nucleus, based on the energy of the electron However, we can only guess within a certain degree of probability the location of an e- The Quantum Model of the Atom • The probability of finding an electron within a certain volume of space surrounding the nucleus can be represented by a fuzzy cloud – The cloud is more dense where the probability of finding the e- is higher. The Quantum Model of the Atom • Each electron in a given atom is given a set of 4 values called quantum numbers, that describe an electron’s behavior. – The 1st 3 quantum numbers map the electron’s location, the 4th describes the electron’s orientation. – No 2 electrons have an identical set of four quantum numbers. The Quantum Model of the Atom • You can assign every electron in a given atom (element) a set of 4 quan- tum numbers • The quantum numbers act as the electron’s address in the atom. • Quantum #’s can be described as a kind of coordinate system to map the location of an e- in the atom. The Quantum Model of the Atom • The problem with e- in the atom is that they can’t be pinned down to a precise location because of Heisen- berg’s Uncertainty Principle – So the quantum #’s only give a fuzzy or probable location of the electron in the atom. The Quantum Model of the Atom • An analogy of quantum numbers might help. – We can think about the quantum #’s as perhaps like trying to find our seat in Rupp Arena using a ticket stub. The Quantum Model of the Atom • Each piece of information on your ticket stub gets you closer and closer to your seat. – Each quantum number gets us closer and closer to the probable location of an electron The Quantum Model of the Atom • The 1st quantum number is the “Principle Quantum Number” – symbolized by n. – can values of 1 to infinity. • The larger the value of n, the farther from the nucleus the electron is. – These electrons are more energetic so the volume of their appearance is larger The Quantum Model of the Atom • Each energy level has a limit to the number of electrons it can hold. – n=1 can hold 2 electrons – n=2 can hold 8 electrons – n=3 can hold 8 electrons – n=4 can hold 18 electrons – n=5 can hold 18 electrons – n=6 can hold 32 electrons The Quantum Model of the Atom • The Principle quantum number can be compared to the level of Rupp. – The Upper Arena is farther from the floor than the Lower Arena – The larger the principal quantum number the farther from the nucleus. The Quantum Model of the Atom • The 2nd Quantum number is the “Azimuthal Quantum number” – Symbolized with an “l,” – can have numbers of 0, 1, 2, 3 which correspond to the letters s, p, d, f. – indicates a shape of an orbital – “l” is expressed with letters rather than numbers. • An s orbital is spherical • A p orbital is dumb-bell • A d is mostly clover-leaf • An f is really complicated The Quantum Model of the Atom • Each l is called an orbital – An orbital is the region or volume around the nucleus of an atom where an electron with a given energy is likely to be found. The Quantum Model of the Atom • Every energy level (quantum # - n) contains 1 and only 1 s sublevel – The number of sublevels in any given n is theoretically related to the value of n • n=1has 1 sublevel…only the s • n=2 has 2 sublevels…s & p • n=3 has 3 sublevels…s, p, & d • n=4 has 4 sublevels…s, p, d, & f The Quantum Model of the Atom • The quantum # l might correspond to the section number on our stub – It narrows down for us to the specific area in the upper arena that our seat is in. – The l quantum number gives us the sublevel of the electron on the energy level. The Quantum Model of the Atom • The 3rd Quantum number is the “Orientation/Orbital quantum number” – Symbolized by ml – Within each sublevel, are orbitals – each with a different orientation. – Each orbital higher than ml = 1 can have a different orientation on the Cartesian axis (x, y, & z) The Quantum Model of the Atom • On a map ml might be thought of as the row our seat is located on. – The row narrows down for us where in the section our seat is. – In the atom, ml gives the direction that the shape of the volume that the electron occupies points. The Quantum Model of the Atom • Together the l and ml quantum numbers give valuable info about the electrons probable location • The “s” sublevel (l =0; ml = 0): – Spherical shape and only one allowed in each energy level. – As the energy increases (n) the “s” orbital also gets bigger. The Quantum Model of the Atom • The p-sublevel: (l =1; ml=-1,0, or 1) – Shaped like a dumbbell. – There are 3 orbitals designated px, py, or pz in each energy level. (Based on axis on the cartesian coordinates) – The p orbitals are higher energy then s orbitals – Only found in ground state atoms containing 5 electrons or more The Quantum Model of the Atom • The d-orbital (l =2; ml= -2, -1, 0, 1, 2): – The d orbitals have more complicated shapes. – There are 5-d orbitals in each energy level that they appear. – The d-orbitals appear only after the 2nd energy level, and beyond Proposed composite of 5 d-orbitals The Quantum Model of the Atom • The f-orbital (l = 3; ml = -3, -2, -1, 0, 1, 2, 3) – Most energetic and complicated – There can be 7 “f” orbitals for each energy level that they occupy. The Quantum Model of the Atom • There is a limit to how many electrons that each sublevel can hold, which limits the number of electrons that can have the same relative energy Sublevel # of Maximum # Orbitals of Electrons s 1 2 p 3 6 d 5 10 f 7 14 The Quantum Model of the Atom • The 4th and final Quantum Number, is the Spin quantum number – Symbolized by ms – Each orbital can hold at most 2 electrons, • They must spin in opposite directions on their axes designated (+½ & -½) The Quantum Model of the Atom • The spin quantum number might work somewhat like the seat number on the ticket stub. – There is only one possible seat that corresponds to the information on your ticket. – There is only one possible electron that matches a given set of quantum numbers The Quantum Model of the Atom Set of (n, l, ml, ms) • H only has 1 electron, and it is on the n=1 energy level, and it’s in the s- sublevel – (1,0,0,+½) • He has 2 electrons, and they are both on the n=1 energy level, and in the s sublevel – (1,0,0,+½)(1,0,0,-½) The Quantum Model of the Atom • Lithium has an electron in the n=2 energy level and so on…. – 3Li: (1,0,0,+½) (1,0,0,-½) (2,0,0,+½) – 4Be: (1,0,0,+½) (1,0,0,-½) (2,0,0,+½) (2,0,0,-½) – 5B: (1,0,0,+½) (1,0,0,-½) (2,0,0,+½) (2,0,0,-½) (2,1,-1,+½) The Quantum Model of the Atom • Continuing With n=2 – 6C: (1,0,0,+½) (1,0,0,-½) (2,0,0,+½) (2,0,0,-½) (2,1,-1,+½) (2,1,0,+½) – 7N: (1,0,0,+½) (1,0,0,-½) (2,0,0,+½) (2,0,0,-½) (2,1,-1,+½) (2,1,0,+½) (2,1,1,+½) The Quantum Model of the Atom – 8O: (1,0,0,+½) (1,0,0,-½) (2,0,0,+½) (2,0,0,-½) (2,1,-1,+½) (2,1,0,+½) (2,1,1,+½) (2,1,-1,-½) – 9F: (1,0,0,+½) (1,0,0,-½) (2,0,0,+½) (2,0,0,-½) (2,1,-1,+½) (2,1,0,+½) (2,1,1,+½) (2,1,-1,-½) (2,1, 0,-½) The Quantum Model of the Atom – 10Ne: (1,0,0,+½) (1,0,0,-½) (2,0,0,+½) (2,0,0,-½) (2,1,-1,+½) (2,1,0,+½) (2,1,1,+½) (2,1,-1,-½) (2,1, 0,-½) (2,1,1,-½) Not every orbital is found in every energy level. (ie.The n=1 level only contains the s orbital) Electron Configurations • The distribution of electrons among the energy levels, sublevels, orientations, and spins of an atom is known as the electron configuration. – Having a basic understanding of how the electrons are configured helps us determine the interaction of atoms of elements to other elements – When they come into contact it’s the outer electrons that do the chemistry. Electron Configurations • Electron configurations are determin- ed by distributing electrons among levels, sublevels, & orbitals, in order of lowest in energy to highest. • We can predict the location of the electrons in the atoms by following 3 important principles: Electron Configurations • The Aufbau Principle – Electrons are added one at a time to the lowest energy orbitals available until all electrons are distributed. – The # of electrons distributed, depends on the atomic # of the atom. – We’ll use a diagram to help placement in the proper order Electron Configurations • The Pauli Exclusion Principle – An orbital can hold a maximum of 2 electrons. – To occupy the same orbital the electrons must spin in opposite directions. • Depicted with arrows orbital pointed in opposite directions. 2 electrons Electron Configurations • Hund’s Rule – Electrons occupying equal-energy orbitals, are distributed so that the maximum number of unpaired electrons results. – For ex, with Nitrogen’s 7 electrons 1 2 2 s s p 4d 5s 4p 3d Energy 4s 3p Oxygen 3s 2p 2s 1s 4d 5s 4p 3d Energy 4s 3p Nickel 3s 2p 2s 1s Electron Configurations • We generally don’t draw the energy pattern and then fill in the boxes for the configurations. We generally use this type of notation: # of electrons Principal in the orbital Energy Level Orbital Type Electron Configurations • We generally don’t draw the energy pattern and then fill in the boxes for the configurations. We generally use this type of notation: # of electrons Principal in the orbital Energy Level Orbital Type Electron Configurations • We generally don’t draw the energy pattern and then fill in the boxes for the configurations. We generally use this type of notation: # of electrons Principal in the orbital Energy Level Orbital Type Electron Configurations • We generally don’t draw the energy pattern and then fill in the boxes for the configurations. We generally use this type of notation: # of electrons Principal in the orbital Energy Level Orbital Type Electron Configurations • We generally don’t draw the energy pattern and then fill in the boxes for the configurations. We generally use this type of notation: # of electrons Principal in the orbital Energy Level Orbital Type Electron Configurations • To help write the electron configura- tions we can use one of two tools. • You choose the one that is most comfortable for you. – The periodic table – The Aufbau diagram hanging in the room Electron Configurations • Fe (Atomic Number = 26) 1s2 2s2 2p6 3s2 3p6 4s2 3d6 • Mg (Atomic Number = 12) 1s2 2s2 2p6 3s2 • Ne (Atomic Number = 10) 1s2 2s2 2p6 • Ti (Atomic Number = 22) 1s2 2s2 2p6 3s2 3p6 4s2 3d2 • Zr (Atomic Number=40) 1s2 2s2 2p6 3s2 3p64s2 3d10 4p6 5s2 4d2 Electron Configurations • Don’t have to write out the entire electron configuration. • There is a short-cut: – Keeps focus on valence electrons – An atom’s inner electrons are represented by the symbol for the nearest noble gas with a lower atomic number. K: [Ar]4s1 Electron Configurations For the element Phosphorus -- 15 electrons 1s22s22p63s23p3 P: [Ne] 3s 23p3 MUST BE A NOBLE GAS Electron Configurations Let’s do a couple more: Ba: [Xe] 6s 2 Hg: [Xe] 6s2 4f14 5d10 V: [Ar] 4s2 3d3 Exceptions to the order of filling Electron Configurations • The chemistry of an atom occurs at the set of electrons called valence electrons • The valence electrons are the outer- most s and p electrons of the atom. – 2 s electrons + 6 p electrons = a full set of valence electrons • The arrangement of the valence e- lead to the elements properties.

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