29A bohr model, h-atom

29A bohr model, h-atom - 5/22/2011 Outline Physics 1C...

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5/22/2011 1 Physics 1C Lecture 29A "Splitting the atom is like trying to shoot a gnat in the Albert Hall at night and using ten million rounds of ammunition on the off chance of getting it. That should convince you that the atom will always be a sink of energy and never a reservoir of energy." --Ernest Rutherford Outline Hydrogen atom Atomic spectra LASER Hydrogen Atom In 1913, Neils Bohr explained atomic spectra by utilizing Rutherford’s Planetary model and quantization. In Bohr’s theory for the hydrogen atom, the electron moves in circular orbit around the proton. The Coulomb force provides the centripetal acceleration for continued motion. Hydrogen Atom Only certain electron orbits are stable. In these orbits the atom does not emit energy in the form of electromagnetic radiation. Radiation is only emitted by the atom when the electron “jumps” between stable orbits. Hydrogen Atom The electron will move from a more energetic initial state to less energetic final state. The frequency of the photon emitted in the “jump” is related to the change in the atom’s energy: If the electron is not “jumping” between allowed orbitals, then the energy of the atom remains constant. Hydrogen Atom Bohr then turned to conservation of energy of the atom in order to determine the allowed electron orbitals. The total energy of the atom will be: But the electron is undergoing centripetal acceleration (Newton’s second law):
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5/22/2011 2 Angular Momentum Recall from classical mechanics that there was this variable known as angular momentum, L . Angular momentum, L , was defined as: L = I ω where I was rotational inertia and ω was angular velocity. For an electron orbiting a nucleus we have that: Giving us: Hydrogen Atom Bohr postulated that the electron’s orbital angular momentum must be quantized as well: where ħ is defined to be h /2π. This gives us a velocity of:
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29A bohr model, h-atom - 5/22/2011 Outline Physics 1C...

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