Postulates of Bohr model Electrons can have only certain specific values of energy. Electrons travel in fixed, circular orbits* (* = we no longer believe this postulate)

Postulates of Bohr model Energy absorbed Energy Released as light When an electron absorbs the exact difference in energy between 2 levels it makes a quantum leap up When an electron makes a quantum leap down it releases the exact difference in energy between two levels.

Link to Electron Orbits

Foundations of Modern Quantum Mechanics Bohr Model (1913) Concept of quantized (restricted, only certain specific allowed) energy levels for electrons.

Quantum Leaps Concept of electron level transitions or QUANTUM LEAPS Accurately predicts visible emission spectra of hydrogen.

Failure of Bohr Model Bohr model does NOT accurately predict emission spectra of any element besides hydrogen. Fatal Flaw: Electrons DO NOT travel in fixed CIRCULAR ORBITS

Foundations of Modern Quantum Mechanics Bohr Model Modern quantum mechanics ACCEPTS quantized energy levels, but REJECTS Bohr’s circular orbits.

Is it possible to determine the exact trajectory of an electron around the nucleus? NO!

Heisenberg Uncertainty Principle Link Heisenberg explained Heisenberg Uncertainty Principle It is impossible to accurately determine both the position and momentum of an electron at the same time. (Momentum = mass x velocity; velocity = speed with a direction). Link to video

Trying to pinpoint the location of a tiny electron requires a collision with short wavelength high energy photon which then changes the speed and direction the electron is traveling in an unpredictable way.

The act of measuring the POSITION changes the MOMENTUM (speed and/or direction.

Implication of Heisenberg Uncertainty Principle The implication of the Heisenberg Uncertainty Principle is that it is IMPOSSIBLE to trace the exact trajectory (path) that an electron will follow.

Implication of Heisenberg Uncertainty Principle It is only possible to describe the PROBABILITY of an electron being in a particular region of space at a particular time.

De Broglie Wave-Particle Duality Louis de Broglie originated the idea that all matter and energy displays properties of both particles (with mass) and waves (with wavelength). Link to Wave-Particle duality

Results of Schroedinger’s Work Schroedinger described the behavior of each electron in an atom by using something called a “wave function”, symbolized by the Greek letter psi: While itself has no physical meaning, 2 corresponds to the probability of finding an electron in a particular region of space (orbital). The requirement of fitting a wave function in a particular region around the nucleus means that only certain wavelengths (and therefore energies) are possible for a given electron. Treating the electron as a standing wave explains why electron energy levels must be quantized! Link to Hydrogen Phet

Standing waves with wavelengths that “fit” in the space

Only certain specific wavelengths of light will fit in the space occupied by the standing wave without destructive interference. De Broglie standing wave video

Since wavelength determines energy, restricted wavelengths means restricted energies.

Schroedinger Equation Results explain why electron energies are QUANTIZED. Only certain specific WAVELENGTHS are possible for standing wave to “fit” in the space around the nucleus with destructive interference collapsing the wave function.

Image of orbital (space in which there is a 90% chance of finding an electron)

Link to Double Slit/ Heisenberg Link to Brian Greene (use first 20 min) Link to Double slit quantum