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Quantum Theory 3

Quantum Theory 3. Section 4-3. Topics. The Bohr Model Summary. The Bohr Model. While working in Rutherford’s lab, Niels Bohr proposed that electrons move in circular orbits about the nucleus. The Bohr Model. Unfortunately, classical physics predicts that such

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Quantum Theory 3

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  1. Quantum Theory 3 Section 4-3

  2. Topics • The Bohr Model • Summary

  3. The Bohr Model While working in Rutherford’s lab, Niels Bohr proposed that electrons move in circular orbits about the nucleus

  4. The Bohr Model Unfortunately, classical physics predicts that such orbits are not stable because the electrons would radiate away their energy and spiral into the nucleus in about 10-8 seconds

  5. The Bohr Model Bohr postulated: 1. electrons can move only in certain orbits without radiating 2. atoms radiate when the electron transitions from one orbit to another and the frequency f of the radiation is given by Ei Ef

  6. The Bohr Model In Bohr’s 1913 paper, he showed that his frequency condition implied that angular momentum is quantized in units of h / 2p Ei Ef

  7. The Bohr Model Newton’s law for circular motion e Electric force Q = Ze Quantization condition from these formulae…

  8. The Bohr Model …it follows that e where Q = Ze is the Bohr radius and is the electric charge of the nucleus

  9. The Bohr Model Assuming the electron speed is small compared with that of light, the total energy of the electron is e Q = Ze Finally, when we substitute the formula for r we get…

  10. The Bohr Model …the total energy of the nth orbit e Q = Ze where

  11. The Bohr Model Therefore Bohr’s frequency postulate e Q = Ze becomes

  12. Energy levels of hydrogen

  13. Summary • The Bohr Model • This was the first successful model of simple atoms like hydrogen • But, unfortunately, its extension to complex atoms was not very successful

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