Parts of Unit 4 part b Electrons and Periodic Behavior Cartoon courtesy of NearingZero.net

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!

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

Electromagnetic radiation propagates through space as a wave moving at the speed of light. C = speed of light, a constant (3.00 x 108 m/s)  = frequency, in units of hertz (hz, sec-1)  = wavelength, in meters

Types of electromagnetic radiation:

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

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

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

Photoelectric Effect animation 10

Excited atom Bohr's Atom: Quantum Behavior in Hydrogen Close   Bohr's Atom: Quantum Behavior in Hydrogen Concept Simulation - reenacts electron's 'jump' and 'fall' to precise energy levels in a hydrogen atom. © 2000 - 2007, Visionlearning, Inc. 11

The energy (E ) of electromagnetic radiation is directly proportional to the frequency () of the radiation. E = h E = Energy, in units of Joules (kg·m2/s2) h = Planck’s constant (6.626 x 10-34 J·s)  = frequency, in units of hertz (hz, sec-1)

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

Quantum Numbers Each electron in an atom has a unique set of 4 quantum numbers which describe it. Principal quantum number (n) = main energy level and number of sublevels (s,p,d,f,) n2 = number of orbits in the sublevels 2n2 = number of total number of electrons Angular momentum quantum number Magnetic quantum number Spin quantum number +1/2 , -1/2

Heisenberg Uncertainty Principle “One cannot simultaneously determine both the position and momentum of an electron.” 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! Werner Heisenberg

Pauli Exclusion Principle No two electrons in an atom can have the same four quantum numbers. Wolfgang Pauli

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: 2n2

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

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

P orbital shape 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.

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” d orbital shapes …and a “dumbell with a donut”!

Shape of f orbitals

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.

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. For n = 3, l can be either 0, 1, or 2. The magnetic quantum number (m) can be any integer between -l and +l. For l = 2, m can be either -2, -1, 0, +1, or +2.

Maximum number of electrons Table 3-6a - Orbital and Electron Capacity for the Four Named Sublevels Sublevel # of orbitals Maximum number of electrons s 1 2 p 3 6 d 5 10 f 7 14

Principle energy level (n) Type of sublevel :    Table 3-6b Orbitals and Electron Capacity of the First Four Principle Energy Levels Principle energy level (n) Type of sublevel Number of orbitals per type Number of orbitals per level(n2) Maximum number of electrons (2n2) 1 s 2 4 8 p 3 9 18 d 5 16 32 f 7

Orbital Energies  29

Remember to start at the beginning of each arrow, and then follow it all of the way to the end, filling in the sublevels that it passes through.  In other words, the order for filling in the sublevels becomes 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d,7p Each time an “s” and a “p” fill (octet = 8) the next energy level starts

Principle, angular momentum, and magnetic quantum numbers: n, l, and ml

Spin Quantum Number Spin quantum number denotes the behavior (direction of spin) of an electron within a magnetic field. Possibilities for electron spin:

Relative Energies for Shells and Orbitals 36

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… Orbital shapes are defined as the surface that contains 90% of the total electron probability.

Orbital filling table

Electron configuration of the elements of the first three series