Chemistry Chapter 4 Arrangement of Electrons in Atoms The 1998 Nobel Prize in Physics was awarded "for the discovery of a new form of quantum fluid with fractionally charged excitations." At the left is a computer graphic of this kind of state.1998 Nobel Prize in Physics

The Puzzle of the Atom Protons and electrons are attracted to each other because of opposite charges Electrically charged particles moving in a curved path give off energy Despite these facts, atoms don’t collapse into the nucleus of the atom but instead “magically” fill up an e- cloud.

Wave-Particle Duality JJ Thomson won the Nobel prize for describing the electron as a particle. His son, George Thomson won the Nobel prize for describing the wave-like nature of the electron. The electron is a particle! The electron is an energy wave!

Confused??? You’ve Got Company! “No familiar conceptions can be woven around the electron; something unknown is doing we don’t know what.” Physicist Sir Arthur Eddington The Nature of the Physical World 1934

The Wave-like Electron Louis deBroglie The electron propagates through space as an energy wave. To understand the atom, one must understand the behavior of electromagnetic waves.

c = ƒ c = ƒ C = speed of light, a constant (3.00 x 10 8 m/s) ƒ ƒ = frequency, in units of hertz (hz, sec -1 ) = wavelength, in meters Electromagnetic radiation propagates through space as a wave moving at the speed of light.

Types of electromagnetic radiation:

Maxwell Planck The energy (E ) of electromagnetic radiation is directly proportional to the frequency (ƒ) of the radiation. ƒ E = h ƒ E = Energy, in units of Joules (kg·m 2 /s 2 ) h = Planck’s constant (6.626 x J·s) ƒ = frequency, in units of hertz (hz, sec -1 )

Long Wavelength = Low Frequency = Low ENERGY Short Wavelength = High Frequency = High ENERGY Wavelength Table

…produces all of the colors in a continuous spectrum Spectroscopic analysis of the visible spectrum…

…produces a “bright line” spectrum Spectroscopic analysis of the hydrogen spectrum…

This produces bands of light with definite wavelengths. Electron transitions involve jumps of definite amounts of energy.

The Bohr Model of the Atom Neils Bohr I pictured electrons orbiting the nucleus much like planets orbiting the sun. But I was wrong! They’re more like bees around a hive. WRONG!!!

Orbital shapes are defined as the surface that contains 90% of the total electron probability. An orbital is a region within an atom where there is a probability of finding an electron. This is a probability diagram for the s orbital in the first energy level…

Schrodinger Wave Equation probability Equation for probability of a single electron being found along a single axis (x-axis) Erwin Schrodinger

Heisenberg Uncertainty Principle You can find out where the electron is, but not where it is going. OR… You can find out where the electron is going, but not where it is! “One cannot simultaneously determine both the position and momentum of an electron.” Werner Heisenberg

The address of the e- determined. {SORT OF…} The Address of the e- comes from the probability of its location in an orbital. Through energy calculations and wave equations the address can be simplified via the following: 1) Bohr diagrams ( e- dot diagrams ) 2) e- configuration notation 3) e- orbital notation 4) Quantum numbers

The s orbital has a spherical shape centered around the origin of the three axes in space. s orbital shape

Orbitals of the same shape (s, for instance) grow larger as n increases… Nodes are regions of low probability within an orbital. Sizes of s orbitals

There are three dumbbell-shaped p orbitals in each energy level above n = 1, each assigned to its own axis (x, y and z) in space. P orbital shape

Things get a bit more complicated with the five d orbitals that are found in the d sublevels beginning with n = 3. To remember the shapes, think of “double dumbells ” …and a “dumbell with a donut”! d orbital shapes

Shape of f orbitals

Quantum Numbers To determine the location of an electron scientists have invented a system to organize each electron found in an atom. The system is based upon the unique energy of each of the atom’s electrons. Each electron in an atom has a unique set of 4 quantum numbers which describe it.  Principal quantum number  Angular momentum quantum number  Magnetic quantum number  Spin quantum number

Pauli Exclusion Principle No two electrons in an atom can have the same four quantum numbers. Wolfgang Pauli No two electrons or objects can exist in the same place at the same time. e-e-e-e- e-e-e-e-

Principal Quantum Number Generally symbolized by n, it denotes the shell (energy level) in which the electron is located. Number of electrons that can fit in a shell: 2n 2

Angular Momentum Quantum Number The angular momentum quantum number, generally symbolized by l, denotes the orbital (subshell) in which the electron is located.

Magnetic Quantum Number The magnetic quantum number, generally symbolized by m, denotes the orientation of the electron’s orbital with respect to the three axes in space.

Spin Quantum Number (s) Spin quantum number denotes the behavior (direction of spin) of an electron within a magnetic field. Possibilities for electron spin: ClockwiseCounter 1 st e-  Clockwise 2 nd e-, 

Assigning the Numbers  The three quantum numbers (n, l, and m) are integers.  The principal quantum number (n) cannot be zero. n must be 1, 2, 3, etc.  The angular momentum quantum number (l) can be any integer between 0 and n - 1. Ex. For n = 3, l can be either 0, 1, or 2.  The magnetic quantum number (m) can be any integer between -l and +l. Ex. For l = 2, m can be either -2, -1, 0, +1, or +2.