The Electromagnetic Spectrum and the Model of the Atom Part II – Quantum mechanics

1. The Electromagnetic Spectrum and the Model of the AtomPart II – Quantum mechanics Chemistry – Mrs. Cameron

2. Bohr’s Model Of The Atom • Electrons move around the nucleus in fixed paths or orbits much like the planets move around the sun • Orbit positions, labeled with the integer n, have specific potential energy • The lowest energy state of an atom is called the ground state (an electron with n = 1 for a hydrogen atom) Heisenberg’s Uncertainty Principle

3. Heisenberg’s Uncertainty Principle • When dealing with particles as small as electrons, the Heisenberg Uncertainty principle must be taken into account. • It is not possible to measure the position and momentum of a moving object and be able to predict its future position. • Collision of the light and electron moves the electron in an unpredictable way

4. Using light and radiation can be difficult… Radiation is much larger than the atoms we seek to study..or..

5. And especially in the case of electrons, The photons can act like a breaking ball on pool table, moving electrons in unpredictable patterns. It is therefore impossible to know the exact position of the electron in the atom

6. A New Model • Must explain the Phenomena of: • Line spectra • Movement of electrons • Quantization of energy • Dual nature of light and matter • Inability to locate electrons Quantum Mechanical Model of the Atom • Explains the properties of atoms by treating the electron as a wave that has quantized energy. • Uses probability to describe the locations of electrons around the nucleus.

7. Electron “Clouds”: • The probability of finding an electron in various locations can be visualized as a blurry cloud. • Least dense where probability is low • More dense where probability is high

8. Atomic Orbital - the region around a nucleus where an electron with a given energy is likely to be found. - draw the surface that encloses 90% probability.

9. Schrödinger Wave Equations: • When treating the electron as a wave, the mathematics is complicated. Schrödinger proposed an equation containing both wave and particle terms. • The mathematics looks at the balance between electrostatic and kinetic energy.

10. Electron Position in Hydrogen - As the electron moves closer to the nucleus, electrostatic energy decreases. - Kinetic energy is increasing because confined to smaller space. (The K.E. of the electron is inversely related to the volume in which it is confined.) - These two effects oppose each other, balance is reached and the atom becomes stable.

11. Wave Equations • Example of the equation in one dimension: d2ψ + 8π2m(E-V) ψ = 0; dx2 h2 • Solving the equation leads to wave functions, . • There are many solutions for ψ, each associated with a set of numbers called quantum numbers.

12. Quantum Numbers, Energy Levels, and Orbitals Principle Quantum #: n = principle energy levels - As n , the energy of the electron increases and it is found further from the nucleus. - n can only take on integral numbers starting with 1 - n=1 is the first principal energy level, etc. - As n becomes larger, the atom becomes larger and the electron is further from the nucleus. - Similar to Bohr’s “n”

13. Angular Momentum Quantum #: l(also known as the azimuthal quantum number) This quantum number defines the shape of the orbital. • Each shape is denoted by a value for l • Depends on the value of n. • The values of l begin at 0 and increase to n – 1. • We usually use letters for l (s, p, d and f for l = 0, 1, 2, and 3). Usually we refer to the s, p, d and f orbitals. • A combination of n and l denote a subshell Ex: “2p” n= 2, l =1

14. Orbitals and Sublevels • Each level of n can have n sublevels. • For example: n = 1 can have 1 sublevel (s) n = 2 can have 2 sublevels (s, p) n = 3, 3 sublevels (s, p, d) n= 4 and higher, 4 sublevels (s,p,d,f)

15. Orbitals and Sublevels • Each sublevel* of n contains a different number of orbitals. • Each orbital can hold 2 electrons *Represented by the secondary quantum # l

16. Orbital shapes •All s orbitals are spherical. •As n increases, the s orbitals get larger.

17. P Orbitals •There are three p orbitals: px, py and pz. •The three p orbitals lie along the x-, y-, and z- axes of a Cartesian system. •The orbitals are dumb-bell shaped; each has two lobes. •As n increases, the p orbitals get larger.

18. D Orbitals There are 5 d orbitals. 4 look like 4-leafed clovers, the other looks like a “double pacifier.”

20. Magnetic Quantum #: ml Determines the direction or orientation in space of the sublevels surrounding the nucleus. Values for mlrange from + l to -l

21. Spin Quantum Number ms - Associated with the magnetic properties of spinning charged particles. ms = ½ ms = - ½ - Spinning charged particles set up a magnetic field.

22. Orbital summary