Lecture 33

Energy and Excitation in Matter

  • Increasing energy in a sample causes various excitations, such as:

    • Rotational excitation (example: microwave ovens where absorbed microwave light causes water molecules to rotate faster, increasing kinetic energy through collisions).

    • Electronic excitation (example: absorption of visible, ultraviolet, or x-ray light excites electrons to higher energy states).

Spectroscopy

  • Spectroscopy experiments are used to observe how different light interacts with matter by checking which light frequencies are absorbed by a sample.

  • Types of spectroscopy include:

    • Microwave spectroscopy

    • Infrared spectroscopy

    • Ultraviolet spectroscopy

    • Electronic excitation is the focus of the current discus sion.

Cesium Atom Example

  • Cesium (Cs) is element number 55, with:

    • 55 protons and 55 electrons in a neutral atom.

    • Organized into electron shells.

  • Initial light source is off; no electrons are counted on the meter when there’s no excitation.

Experiment with Light and Electrons

  • Objective: Use light to jiggle an electron out of a cesium atom.

    • Start with red light:

    • Light applied does not cause electron ejection, nothing is detected on the meter.

    • Increase intensity (brightness) of red light:

    • Still no electrons detected, possibly due to low energy of red light.

    • Switch to blue light:

    • Blue light excites electrons, and some electrons are detected on the meter, indicating successful ejection.

Wave Model vs. Photon Model

  • The failure of the wave model (represented by increasing brightness not leading to electron ejection) leads to:

    • Introduction of a new concept by Albert Einstein: Photon.

  • Photon Definition: A particle of light whose energy is determined by frequency (or wavelength) rather than amplitude.

    • Energy of a photon can be defined as:
      E=h<br>uE = h<br>u

    • Where:

      • $E$ = energy of the photon,

      • $h$ = Planck's constant,

      • $
        u$ = frequency of the photon.

  • Analogy:

    • Throwing a ping pong ball (low energy) versus a baseball (high energy); the effect of the object depends on its energy.

Photoelectric Effect

  • The photoelectric effect occurs when light causes the ejection of electrons from a material.

  • The minimum energy threshold for ejection varies depending on the element. Once that energy is exceeded, any excess energy appears as kinetic energy of the ejected electrons.

  • Example threshold:

    • If the energy of light is 500 kJ/mol and the minimum threshold is 100 kJ/mol, then the excess energy of 400 kJ/mol shows as kinetic energy of the electrons:
      KE=Eextlight−EextthresholdKE = E_{ ext{light}} - E_{ ext{threshold}}

Practice Problem on Electron Ejection

  • Given:

    • Energy of light shining on potassium = 3.1 electron volts (eV).

    • Kinetic energy of emitted electrons = 1.1 eV.

  • To calculate the minimum threshold energy:

    • Threshold energy = Energy of light - Kinetic energy = 3.1 eV - 1.1 eV = 2 eV.

Photoelectron Spectroscopy

  • Shining photons onto a sample to measure ejected electrons, providing data about energy thresholds, known as binding energies or ionization energies.

  • Binding energy is the energy needed to remove an electron from its atom:

    • Ionization energy: the energy absorbed to remove an electron, measured in kJ/mol.

Atomic Examples

  1. Hydrogen: Ionization energy calculated at 13.6 kJ/mol.

  2. Helium: Second element, has greater attraction due to additional protons, requiring 2372 kJ/mol for ejection.

  3. Lithium: Shows two ionization energies due to different binding energies:

    • Two close electrons have a stronger attraction and a different ionization energy than the one further away.

    • Two peaks in the spectrum represent the core electrons and the valence electron.

    • Ejection caused by photon energy measurements can provide ratios of ejected electrons.

  4. Beryllium and Boron: Beryllium (element 4) has a subshell arrangement causing more tightly held electrons than boron (element 5), indicating different ionization procedures.

Subshell Model and Periodicity

  • Advances in atomic model to include subshell structures based on observed data.

  • Electrons in shells:

    • Shell 1: 2 electrons;

    • Shell 2: 2 (s subshell) + 6 (p subshell) = 8 total;

    • Shell 3: 10 total.

  • Predict ionization energies based on $ ext{Z}_{ ext{effective}}$ derived from protons and electron shielding.

General Trends

  • Ionization energy increases left to right across a period.

  • Anomalies appear due to subshell filling and effective nuclear charge dynamics impacting energy levels.

  • Important peaks in a photoelectron spectrum indicate the number of electrons, and the heights of peaks represent relative population sizes of those electrons.