Modern Theory of the Atom Quantum Mechanical Model Or Wave Mechanical Model Or Schrodinger’s Model

source

Recap of Bohr Model Electrons treated as particles moving in circular orbits. Specify speed, position, energy. Quantization of energy levels is imposed. Ground state: electrons close to nucleus Electron transitions between energy levels can occur. Higher energy levels are farther from nucleus. –Moving up, electron absorbs energy –Moving down, electron emits light energy Wavelengths of light in H spectrum can be predicted. Depend on energy difference of 2 levels involved in transition.

source

Problems with Bohr Model Only worked for 1-electron systems. Quantization of energy levels had to be “imposed.”

1924: De Broglie Proposed that if light can show both particle and wave behavior, maybe matter can too.

Every wavelength of light has its own unique frequency and its own unique energy.

2 kinds of waves Traveling wave Wave is not confined to a given space Travels from one location to another Interrupted by a boundary or another wave Standing wave Confined to a given space. (Ends pinned.) Interference between incident & reflected waves. At certain frequencies, certain points seem to be standing still. Other points, displacement changes in a regular way.

Traveling Wave #1 Traveling Wave #2

Guitar string Standing wave #1

DeBroglie Electron-Wave The wavelength describing an electron depends on the energy of the electron. At certain energies, electron waves make standing waves in the atom. The wave does not represent electron path.

Guitar vs. Electron In the guitar string, only multiples of half- wavelengths are allowed. For an orbiting electron, only whole numbers of wavelengths allowed. = h/mv Where h=Planck’s constant, m=mass, v=velocity

Modern Theory Electron is treated as a wave. Cannot specify both position & velocity of electron. Can determine probability of locating the electron in a given region of space. Quantized energy levels arise naturally out of wave treatment. Also called Quantum Mechanics or Wave mechanics. Scienties = Schrodinger.

Schrödinger’s Equation Ĥ  = E  Solve for , the wave functions.  2 gives the probability of finding an electron near a particular point in space. –Represented as probability distribution or electron density map.

Heisenberg uncertainty principle Fundamentally impossible to know the velocity and position of a particle at the same time. Impossible to make an observation without influencing the system. –A photon colliding with an electron will knock it off its path.

Bohr Model vs. Modern Theory Electron = particle Orbit Holds 2n 2 electrons Spherical Each orbit has a specific energy Can find position, speed Electron = Wave Orbital Holds 2 electrons Not necessarily spherical Each orbital has a specific energy Probable location

Orbital – Modern Theory Orbital = term used to describe region where an electron might be. Each orbital has a specific energy and a specific shape. Each holds 2 electrons. Described by 4 parameters in the wave function – quantum numbers = n, l, m, s – like an address

s orbitals (  2 )

p orbitals

d orbitals

What can orbitals do for us? Physical structure of orbitals explains –Bonding –Magnetism –Size of atoms –Structure of crystals

Quantum Numbers Each electron in an atom has a set of 4 quantum numbers – like an address. –3 quantum numbers describe the orbital –1 quantum number gives the electron spin No two electrons can have all 4 quantum numbers the same. (Pauli exclusion principle)

Energy Level Diagram Energy Level Diagram Energy levels for Polyelectronic atom

n: principal quantum number Related to size and energy of orbital n has integral values: 1, 2, 3, 4, … As n increases, the orbital becomes larger & the electron spends more time farther from the nucleus, which also means higher energy.

l = angular momentum quantum number Related to shape of orbital. l has integral values from 0 to n -1 for each value of n. Orbitals with different shapes have slightly different energies. Each type of orbital resides on a different sublevel of the principle energy level.

l = angular momentum quantum number Principal energy levels are made up of sublevels. The number of sublevels depends on the principal energy level. – 1 st principal energy level has 1 sublevel – 2 nd “ “ “ “ 2 “ – 3 rd “ “ “ “ 3 “ – 4 th “ “ “ “ 4 “, etc.

Naming sublevels Sublevels are usually labeled s, p, d, or f instead of using more numbers. If l = 0, call it an s orbital. If l = 1, call it a p orbital. If l = 2, call it a d orbital. If l = 3, call it an f orbital.

m l = magnetic quantum number m l related to orientation of orbital in space relative to other orbitals in the atom. m l has integral values between l and -l, including 0. –For n = 1, l = 0 and m l = 0. –For n = 2, l = 0 or 1. If l = 0 then m l = 0 If l = 1, then m l = -1, 0, or +1.

orbitals Sublevels are made up of orbitals Each kind of sublevel has a specific # of orbitals Sublevel# of orbitals s1 p3 d5 f7

Spin quantum number, m s m s describes the spin state of the electron in the orbital. m s has two possible values: + ½ and – ½ Pauli exclusion principle: No two electrons in the same atom can have all 4 quantum numbers the same. So each orbital can hold only two electrons.

Orbitals Each orbital can hold two electrons with opposite spins. –s sublevels, 1 orbital: 2 e - max capacity –p sublevels, 3 orbitals: 6 e - –d sublevels, 5 orbitals: 10 e - –f sublevels, 7 orbitals: 14 e -

Prin.En.LevSublevels# orbitals/slTotal # elec 1s12 2s12 p36 3s12 p36 d510 4s12 p36 d510 f714

1 st principal energy level, 1 sublevel – s 2 nd principal energy level, 2 sublevels – s & p 3 rd principal energy level, 3 sublevels Each box represents an orbital and holds 2 electrons.

Order of fill: Aufbau principle Each electron occupies the lowest orbital available Learn sequence of orbitals from lowest to highest energy Is some overlap between sublevels of different principal energy levels

Diagonal Rule 1s 2s 2p 3s 3p 3d 4s 4p 4d 4f 5s 5p 5d 5f 6s 6p 6d 6f 7s 7p Sequence of orbitals: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, … Follow the arrows Exceptions do occur: half-filled orbitals have extra stability.

Hund’s Rule !Distribution of electrons in equal energy orbitals: Spread them out as much as possible! Also, all electrons in singly occupied orbitals must have the same spin state.

Electron Configurations

Compare Bohr & Schrodinger

Frequencies in Chemistry

Electron Configuration & P.T.

Principle Energy Levels  Sublevels Orbitals Hold 2 Electrons Max   n = 1,2,3,4 Holds 2n 2 Electrons max  1 st energy level has 1 sublevel : s 2 nd “ “ “ 2 sublevels : s and p 3 rd “ “ “ 3 “ : s, p, and d 4 th “ “ “ 4 “ : s, p, d, and f s sublevel holds 1 orbital p sublevel holds 3 orbitals d sublevel holds 5 orbital f sublevel holds 7 orbitals 