Introductory Video Quantum Mechanics Quantum Mechanics

IB Assessment Statements  Topic 13.1, Quantum Physics: Atomic Spectra and Atomic Energy States Outline a laboratory procedure for producing and observing atomic spectra Explain how atomic spectra provide evidence for the quantization of energy in atoms Calculate wavelengths of spectral lines from energy level differences and vice versa.

IB Assessment Statements  Topic 13.1, Quantum Physics: Atomic Spectra and Atomic Energy States Explain the origin of atomic energy levels in terms of the “electron in a box” model Outline the Schrödinger model of the hydrogen atom Outline the Heisenberg uncertainty principle with regard to position- momentum and time-energy.

Objectives  Describe emission and absorption spectra and understand their significance for atomic structure  Explain the origin of atomic energy levels in terms of the ‘electron in a box’ model  Describe the hydrogen atom according to Schrödinger  Do calculations involving wavelengths of spectral lines and energy level differences

Objectives  Outline the Heisenberg Uncertainty Principle in terms of position-momentum and time- energy

Atomic Spectra  The spectrum of light emitted by a material is called the emission spectrum.

Atomic Spectra  When hydrogen gas is heated to a high temperature, it gives off light  When it is analyzed through a spectrometer, the light is split into its component wavelengths

Atomic Spectra Different gases will have emission lines at different wavelengths Wavelengths emitted are unique to each gas

Atomic Spectra Mercury This is called the emission spectrum of the gas By identifying the wavelengths of light emitted, we can identify the material

Atomic Spectra Helium A similar phenomenon occurs when we pass white light through a gas On a spectrometer, white light would show a continuous band of all colors

Atomic Spectra Argon When passed through a gas, dark bands appear at the same frequencies as on the emission spectrum This is called the absorption spectrum of the gas

Atomic Spectra - Absorbtion

Atomic Spectra Neon By trial and error, Johann Balmer found that wavelengths in hydrogen followed the formula, But nobody could figure out why But it did show the frequencies were not random

Atomic Spectra  Conservation of energy tells us that the emitted energy will be equal to the difference in atomic energy before and after the emission  Since the emitted light consists of photons of a specific wavelength, the energy will be discrete values following the formula,

Electron In A Box de Broglie Wavelength

Electron In A Box  Amplitude is zero at ends of the box  Since electron can’t lose energy, the wave in the box is a standing wave with fixed nodes at x = 0 and x = L

Electron In A Box

The result is that electron energy is always a multiple of a discrete or quantized value The same principle applies for electrons surrounding a nucleus

Schrödinger Theory  Wave Function, Ψ(x,t)  Schrodinger equation for hydrogen  Separate equations for electrons in every type of atom  Result is that the energy of an electron in a specific atom is quantized

Schrödinger Theory  Schrodinger’s Theory applied to the electron in a box model yields the following data for a hydrogen atom  Energy is discrete or quantized to one of the energy levels given by n = 1, 2, 3

Schrödinger Theory  Energy levels of emitted photons correspond to energy level changes of electrons  Each time an electron drops in energy level, a photon is released with that energy

Schrödinger Theory  Since E = hf, the photon will have a discrete frequency according to its energy  Knowing the energy level change of the electron, we can compute the frequency and vice versa

Schrödinger Theory Max Born Interpretation  | Ψ(x,t)| 2 will give the probability that an electron will be near position x at time t

Schrödinger Theory  Schrodinger’s Theory also predicts the probability that a transition will occur (| Ψ(x,t)| 2 )  Explains why some spectral lines are brighter

Heisenberg Uncertainty Principle  Applied to position and momentum:  Basis is the wave-particle duality  Can’t clearly explain behavior based on wave theory or classical mechanics

Heisenberg Uncertainty Principle  It is not possible to simultaneously determine the position and momentum of something with indefinite precision

Heisenberg Uncertainty Principle  Making momentum accurate makes position inaccurate and vice versa  As Δp approaches 0, Δx approaches infinity  As Δx approaches 0, Δp approaches infinity

Heisenberg Uncertainty Principle  Think of aiming a beam of electrons through a thin slit  Like polarization, we limit wave passage through the slit to a vertical plane  However, the wave will diffract which changes the horizontal position

Heisenberg Uncertainty Principle  Even though vertical position is fairly certain, change in horizontal position means a change in momentum because of the change in the horizontal component of the velocity

Heisenberg Uncertainty Principle  Applied to energy and time:  The same principle can be applied to energy versus time

Putting It All Together  Unique emission and absorption spectra show that electrons exist at discrete energy levels  The frequency/wavelength of emitted / absorbed light is a function of the electron’s energy level  Since each element has unique electron energy levels, the light it emits/absorbs is unique to that element

Putting It All Together  Schrödinger developed a wave function, Ψ(x,t), to describe electron position vs. time in hydrogen  Wave functions different for each element  Born gave us the probability of finding an electron at a given point at a given time as |Ψ(x,t)| 2

Putting It All Together  But Heisenberg showed that trying to find the electron is difficult

Σary Review  Can you describe emission and absorption spectra and understand their significance for atomic structure?  Can you explain the origin of atomic energy levels in terms of the ‘electron in a box’ model?  Can you describe the hydrogen atom according to Schrödinger?

Σary Review  Can you do calculations involving wavelengths of spectral lines and energy level differences?  Can you outline the Heisenberg Uncertainty Principle in terms of position-momentum and time-energy?

IB Assessment Statements  Topic 13.1, Quantum Physics: Atomic Spectra and Atomic Energy States Outline a laboratory procedure for producing and observing atomic spectra Explain how atomic spectra provide evidence for the quantization of energy in atoms Calculate wavelengths of spectral lines from energy level differences and vice versa.

IB Assessment Statements  Topic 13.1, Quantum Physics: Atomic Spectra and Atomic Energy States Explain the origin of atomic energy levels in terms of the “electron in a box” model Outline the Schrödinger model of the hydrogen atom Outline the Heisenberg uncertainty principle with regard to position- momentum and time-energy.

Homework #1-15