Module 2.2 The Bohr Model

Describe the simplest atom as presented by Ernest Rutherford

• Hydrogen:
  • single proton and nucleus
  • Single moving electron

What does electrostatic force attracting the electron to proton depends on?

• Only the distance between 2 particles

Why is the Bohr model planetary description of an atom incomplete?

• Because e- moving in elliptical orbit would be chaining direction & should continuously emit electromagnetic (EM) radiation
• What eventually happens?
  • E- orbit gets eventually smaller until it spirals into the nucleus, implying atoms unstable

How did Niels Bohr attempt to resolve the paradox?

• Incorporate Planck’s classical physics description of quantization & Einstein’s photos equal to light whose energy (E) is proportional to frequency

What did Bohr assume?

• That e- orbiting nucleus would not emit radiation , but instead emit/absorb photon (single particle of light) and move it to a different orbit

What is Bohr’s Atom Model Equation?

• 
• what is h
  • Planck's constant (fundamental in quantum mechanics)
    • 6.626 x 10^-34 J

Describe ground electronic state

• Orbital w/lowest energy (E), n=1

What happens if the atom receives E from the outside?

• It moves up a higher orbital (excited state)

What happens to the amount of E when e- goes back to initial state?

• the same amount that went in is expelled
  • Law of Conservation

What did Bohr notice about E and e- distance?

• the greater the energy (n increase) the further the orbit from the nucleus
  • conversely, this makes the e- more prone to donation because electrostatic attraction w/nucleus decreases
    • n --> ∞, E approaches zero and e- is removed from nucleus

Blackbody radiation, photoelectric effect, hydrogen atom paradoxes solved, and all involves Planck's constant, what became clear?

• classical physics didn't work for these

Why was Bohr's model flawed?

• it was still based on classical mechanics notion of precise orbits
  • only worked for H

What did Bohr base his model on?

• that electrons orbited nucleus only at a precise distance from the nucleus, directly proportional to E of e-
• these "precise" orbits were named by an orbital, n
  • seen as discrete quantized energy that could only jump (or fall) to a neighboring quantized energy (n = 1 to n = 2 only)
• what made this model fundamentally flawed?
  • it only worked on hydrogen
    • classical physics with set distances doesn't work, eventually it had to be explained using quantum mechanics

Example: Calculating the E of e- in a Bohr Atom

• what is the formula?
  • 
  • what is k?
    • Coulomb's constant - relates to discrete energies to e- orbitals ()
      • 2.179 x 10^-18 J
  • don't forget that there is a negative in front of the En, but when you apply the | Ef - Ei | absolute value, the energy in J will be positive
  • what is n
    • the level of the orbital

Example: Calculating the Energy & Wavelength of Electron Transitions

• it is asking for energy (J) and wavelength (m)
  • First solve for E , which will will end up being positive J
  • Then rearrange wavelength to equal hc/E to solve (using the E you solved in previous equation). Wavelength will use c, speed of light (2.998 x 10^8 m/s) and Planck's constant

What does Bohr model not account for?

• electron-electron interactions in atoms w/more than one electron

What important features does it introduce?
- energy levels of e- in an atom are quantized
- quantum numbers: integers that describe electron arrangement (orbitals?)
- electrons become more energetic once they go farther from the nucleus
- quantized electronic energies are emitted by elements in excited state

Which feature is the most important?

• quantized energy levels