8 Review from Chemistry of Application of Conservation of Energy to Photons and
8 Review from Chemistry of Application of Conservation of Energy to Photons and Atoms
Review of Connecting Conservation of Energy to the Wave and Particle Natures of Light in the Context of the Hydrogen Atom from Chemistry[1]
Instructor’s Notes
NOTE: This is review. If you are familiar with this material, feel free to skip to the problems at the end!
What we expect you to know from this review:
- Electrons in atoms have discrete energy levels.
- In order for an electron to transition from one level to another it must absorb or emit a photon with the exact amount of energy that corresponds to the energy difference. If the energy does not exactly match, then the transition will not occur.
- If I know the energy difference, I can solve for the wavelength of the emitted photon.
- Be familiar with the idea of energy level diagrams such as the one shown below
- The difference in energy levels in a hydrogen atom is
where is the Rydberg constant .
Following the work of Ernest Rutherford and his colleagues in the early twentieth century, the picture of atoms consisting of tiny dense nuclei surrounded by lighter and even tinier electrons continually moving about the nucleus was well established. This picture was called the planetary model, since it pictured the atom as a miniature “solar system” with the electrons orbiting the nucleus like planets orbiting the sun. The simplest atom is hydrogen, consisting of a single proton as the nucleus about which a single electron moves. The electrostatic force attracting the electron to the proton depends only on the distance between the two particles. This classical mechanics description of the atom is incomplete, however, since as described in Basics of Light: Where does Light Come From? an electron moving in an orbit would be accelerating (by changing direction) and, according to classical electromagnetism, it should continuously emit electromagnetic radiation. This loss in orbital energy should result in the electron’s orbit getting continually smaller until it spirals into the nucleus, implying that atoms are inherently unstable.
In 1913, Niels Bohr attempted to resolve the atomic paradox by ignoring classical electromagnetism’s prediction that the orbiting electron in hydrogen would continuously emit light. Instead, he incorporated into the classical mechanics description of the atom Planck’s ideas of quantization and Einstein’s finding that light consists of photons whose energy is proportional to their frequency (Basics of Light: Introduction to the Photon). Bohr assumed that the electron orbiting the nucleus would not normally emit any radiation (the stationary state hypothesis), but it would emit or absorb a photon if it moved to a different orbit. The energy absorbed or emitted would reflect differences in the orbital energies according to this equation:
In this equation, h is Planck’s constant and Ei and Ef are the initial and final orbital energies, respectively. The absolute value of the energy differen