Notes 6-3: Wave/Particle Duality & Quantum Mechanical Model of Atom – Bohr model had limitations

§ Could explain only hydrogen atom § Could not account for chemical behavior or spectra of other elements § Could not explain why energy levels are quantized

1) Light as a wave:

• When light propagates (travels) it behaves as a wave

2) Light as a particle: Has a precisely determined location, but has less certain energy (wavelength) a) Photoelectric Effect: When light shines on a metal, sometimes electrons are ejected from metal.

*Simulation of photoelectric effect from https://phet.colorado.edu/en/simulation/photoelectric • For each metal, there is a minimum frequency of light that is needed to eject an electron.

o If light has a lower frequency than minimum frequency threshold, no electrons are ejected regardless of the light intensity.

o If light has a higher frequency than the minimum frequency threshold, electrons move faster when ejected.

• Increasing the intensity of light only increases the number of electrons ejected, not energy.

Conclusion: • Light is acting like a particle because a discrete

“bundle of needed energy” must hit an electron to eject it. That “bundle of energy” must hit all at once at the location of the electron. This “bundle of energy” is called a photon—a particle, or quantum (smallest amount) of light.

• Higher intensity light consists of more photons. Thus, increasing the intensity of light shining on a metal will eject more electrons, but not faster electrons.

b) Bright Line Emission Spectra: (gas discharge tubes such as Neon lights) • A limited number of distinct frequencies of light are emitted when electrons in atoms first

excited to, “drop down” (relax) from higher energy levels to lower energy levels. • Conclusion: Since an electron loses a distinct amount of energy when it “falls down” from a

higher energy level to a lower energy level, it emits a photon with that same amount of energy (frequency, wavelength). Thus, light is being emitted or absorbed as a discrete “bundle of energy” or as a particle of light.

3) Electrons as waves: Have a precisely determined energy (wavelength), but less certain location. a) Electrons can only have certain wavelengths

(energies) to “fit” onto Bohr orbits: § Wave on left does not fit onto orbit, so

electron can’t have this energy § Wave on right fits with integer number of

wavelengths, this energy is allowed. b) Every particle has a wavelength. However, the

more massive a particle, the smaller the wavelength. Thus, one only notices wave-like properties for particles with extremely small masses (such as electrons, protons, neutrons.)

4) Heisenburg Uncertainty Principle For a good description: Watch video, “What is the Heisenberg Uncertainty Principle?” by Chad Orzel (https://youtu.be/TQKELOE9eY4). For a little extra fun (optional), you can also watch the video on “Schrödinger’s Cat by Orzel (https://youtu.be/UjaAxUO6-Uw). (Videos embedded on my website) a) Definition: It is impossible to know simultaneously the exact position and momentum of a particle.

Heisenburg stated the principle somewhat differently saying: “The more precisely the position is determined, the less precisely the momentum [energy] is known in this instant, and vice versa.” --Heisenberg, uncertainty paper, 1927

b) Heisenburg’s Uncertainty Principle applies to all objects but is only important for very small objects.

The uncertainty for a large item is much smaller than can be measured 5) Schrödinger Wave Functions

a) Schrödinger separately derived wave functions (y), describing distribution and energy of submicroscopic particles • y2 is the probability of finding a particle in a certain region

of space (right) b) Applied to electrons to derive atomic orbitals

• Represent density distribution function of electron • Different from Bohr model’s orbits: probability of finding

an electron in a region of space rather than exact spherical path • We do not know the exact path or movement of the

electron, but we know its energy.

Orbitals: Electrons do not “orbit” in a defined path around the nucleus. Instead, for a particular energy electron, one can only know the most probable locations to find the electron. Thus, we say that electrons are in orbitals. • On the right are two probability maps of an

electron, one in an s and one in a p orbital. Each map shows where that one electron is most likely to be found.

s orbital p orbital

• An orbital is drawn as the surface that encloses 90% of the probability density: