Unit 3 – Electron Configurations Part C: Quantum Mechanical Model Dr. Chin Chu River Dell Regional High School

Background Problem With the Bohr Model – Why and how could the electron in hydrogen orbit in only a small number of allowed paths? Solving the Problem 1. Louis de Broglie – electrons have a dual nature - they can act like particles or waves !!!

All important attributes for particles. Duality of Electrons Cathode Ray Tube Experiment (by JJ Thomson): Electrons travel at high speed. Electrons have fixed mass. All important attributes for particles.

Electron beam behaves like waves. Duality of Electrons Electron beam behaves like waves.

Heisenberg Uncertainty Principle How can police tell the speed of a moving vehicle?

Heisenberg Uncertainty Principle How can we tell the speed of a moving electron? After Before Photon changes wavelength Photon Electron Changes Velocity Moving Electron

Heisenberg Uncertainty Principle Both the velocity and position of a particle (electron) can not be measured at the same time. Werner Heisenberg 1901-1976

Quantum Mechanical Model Schrodinger – developed equations that treat electrons in atoms like waves. describe the shapes of the orbitals in which electrons have a high probability of being found. quantum theory – mathematical explanation for the wave properties of electrons that apply to all atoms. Erwin Schrodinger 1887-1961

Quantum Mechanical Model The nucleus is found inside a blurry “electron cloud” A area where there is a chance of finding an electron

Principles of the Quantum Model Electrons act like waves and particles. Probability of an electron being found at various distances from the nucleus. orbitals – a 3-D region about the nucleus where a specific electron may be found.

Principles of the Quantum Model Electrons have greater energy as their distance from the nucleus increases. Energies of orbitals are quantized within main energy levels. The exact location of electrons can not be pinpointed – they are found in regions of high probability called orbitals or electron clouds.

Similarities -Bohr and Quantum Model The closer the orbital to the nucleus the lower the energy. To move from a lower to a higher level the energy absorbed must be equal to the difference between the levels. When e- drops from a higher to lower level electromagnetic radiation is emitted equal to the difference in energy levels. The most probable location of the e- is a distance equal to the lowest energy level.

Quantum Mechanical Model According to Schrödinger’s calculations, four quantum numbers are needed to fully resolve the wave function mathematically for each electron in any given atom. Meaning – there is a unique set of four quantum numbers to fully describe the behavior of an electron.

Four Quantum Numbers Principal Quantum Number (n) main energy level B. Orbital Quantum Number (l) shape of orbital (s, p, d, f) C. Magnetic Quantum Number (m) orientation of orbital about the nucleus D. Spin Quantum Number (s) indicates clockwise or counter-clockwise spin of the electron (+½ or –½)

Summary Wave and particle duality of electrons. Heisenberg Uncertainty Principle. Schrodinger’s Quantum Mechanical Model of Atoms.