Bohr's Atomic Model

Rutherford, explain!

Accelerating charges ought to loose energy in the form of γ rays.

What, then, makes the atom stable?

Rutherford, explain!

Even if the atom did loose energy, it should have been continuous...

... which it wasn't.

We need a better theory.

Bohr's Postulates

1. Electrons in atoms orbit the nucleus in circular orbits.
2. There exists discrete stationary orbits in which the electrons orbit stably without radiating.
   • It turns out that the angular momentum of these orbits are multiples of ħ
3. When electrons jump from orbit to orbit, they emit/lose energy according to Plank radiation.

Radius

• Equating Centrapetal Force and Electric Force,

  

• From Bohr's second postulate,

  

• Therefore,

  

• And we have the radius,

  

Velocity

Plugging in the radius gives the velocity,

Energy

• Kinetic Energy:

  

• Potential Energy:

  

• Total Energy:

  

Matter Waves

• Matter does behave like a wave, in some sense.
• deBroglie hypothesised that the associated wavelength of a particle is given by λ = h/p

Matter Waves

Seen carefully enough, electrons produce diffraction patterns.

deBroglie's Justification

• Bohr's orbitals are stationary states where the wave function does not evolve.
• Consider an electron wavicle of n wavelengths wrapped around a Bohr orbit.

Not the end...

• Still too many spectral lines
• What if there is more than one electron?
• Too classical: Newtonian mechanics is hardly a good way to describe phenomenon at the quantum level.

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