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Orbital Shapes & Sizes

Orbital Shapes & Sizes. Bohr’s Model & Beyond. What we learned. Quantized Energy For electrons as well as atoms & molecules Absorb/ Emit Quantized Energy. What we learned. Quantized Energy For electrons as well as atoms & molecules Absorb/ Emit Quantized Energy

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Orbital Shapes & Sizes

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  1. Orbital Shapes & Sizes

  2. Bohr’s Model & Beyond

  3. What we learned • Quantized Energy • For electrons as well as atoms & molecules • Absorb/ Emit Quantized Energy

  4. What we learned • Quantized Energy • For electrons as well as atoms & molecules • Absorb/ Emit Quantized Energy By shooting atoms with specific λ light we can detect change in energy ΔE=ΔE=

  5. Schrodinger • Found Quantum numbers for H • Had to approximate electron as a standing wave • Means must have one node

  6. Schrodinger “It is a differential equation that need not be memorized or Even Understood …”

  7. Schrodinger • Took existing equation for a standing wave • Modified to Use de Broglie’s restrictions on wavelength • Energy Levels of H • Results correlated with experiment data • Solutions produce a set of three “Quantum Numbers”

  8. Quantum Numbers The Principle Quantum Number n – tells main shell that we are looking at Value must be greater than 0 n=1, 2, 3, 4,…

  9. Quantum Numbers Angular Momentum Quantum Number ℓ - tells which subshell of n we are looking at, also tells us the shape of the region of space an electron might occupy Value of ℓ must be non-negative and 1 less than n ℓ= 0, 1, 2, …, (n-1)

  10. Quantum Numbers Each value of ℓ is given a letter distinction ℓ 0 1 2 3 Letter s p d f Letters come from spectroscopy. s- sharp, p-principle, d-diffuse, f-fundamental

  11. Quantum Numbers Each value of ℓ is given a letter distinction ℓ 0 1 2 3 Letter s p d f Letters come from spectroscopy. s- sharp, p-principle, d-diffuse, f-fundamental

  12. Quantum Numbers Magnetic Quantum Number mℓ - designates a specific orbital in a subshell, orbitals differ in orientation not in energy Values of mℓ range from –ℓ to + ℓ mℓ= –ℓ, …, -2, -1, 0, 1, 2, …, +ℓ

  13. Quantum Numbers The Spin Quantum Number ms – refers to the spin of an electron and the magnetic field the spin produces Value of ms is for every combination of n, ℓ, and mℓ Schrodinger did not get ms, had to wait for Dirac who modified with relativity

  14. Atomic Orbital n= 1, 2 – normally only highest given ℓ = 0, 1 mℓ = -1, 0, +1 __ __ __ __________

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