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Principle Quantum Numbers

Principle Quantum Numbers. No two electrons in an atom can have the identical sets of quantum numbers: Wolfgang Pauli. Quantum Numbers. Necessary to describe the position, spin, energy and orientation of an orbital in space. Principal quantum number, n. Same n = same main energy level

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Principle Quantum Numbers

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  1. Principle Quantum Numbers No two electrons in an atom can have the identical sets of quantum numbers: Wolfgang Pauli

  2. Quantum Numbers • Necessary to describe the position, spin, energy and orientation of an orbital in space.

  3. Principal quantum number, n • Same n = same main energy level • Related to size of the wave: the higher the n the further the wave extends form the nucleus • The greater the distance from the nucleus • Higher n = higher energy

  4. Secondary Quantum Number • Divides shells into smaller groups of orbitals (sublevels) • The value of n determines which values of l are allowed • l can range from l=0 to l=(n-1)

  5. Sublevels (l)

  6. Magnetic quantum number, ml • Value indicates the individual orbitals within a shell • And the way that they are oriented to each other in space • Values can only range from +l to –l

  7. Spin Quantum Number, ms • Electrons behave like tiny charges that can spin in one of two directions • The spinning electrical charge of an electron creates its own magnetic field • Values can only be: ms= +1/2 or ms= -1/2 • The actual values are not important to us…just the fact that there are 2 separate values • Relates to Hund’s rule

  8. Spin Quantum Number, ms • It is denoted by ‘s’. • It has only two possible values. • s = +1/2 , S = -1/2 • s = +1/2 for clockwise spin. • s = -1/2 for anti-clockwise spin. • An electron spinning clockwise is indicated by (↑) and anti-clockwise by (↓)

  9. Summary of Relationships among Quantum Numbers Reference: Brady and Senese, 5th edition, 2009

  10. Quantum Numbers Video

  11. Practice • What are the possible values for l and ml when n=2?

  12. Practice • What are the possible values for l and ml when n=2?

  13. Practice 2 • What are the quantum numbers in the 4d sublevel?

  14. Practice 2 • What are the quantum numbers in the 4d sublevel?

  15. Practice 3 • What are the set of quantum numbers for the last electron in aluminum?

  16. Practice 3 • What are the set of quantum numbers for the last electron in aluminum?

  17. Review of Bohrs Model and Emission Spectra

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