4강. 오비탈(orbital)이란?👀⎥보어 원자모형의 한계점⎥오비탈을 양자수로 나타내는 방법✍🏻

Scientific Concepts, Discoveries, and Nature Phenomena Presented

1) Bohr’s Atomic Model (and Its Limits)

• Electrons occupy “electron shells” around an atom.
• Energy quantization: when an electron moves from an outer shell to an inner shell:
  • the electron’s energy decreases
  • the atom emits light
  • the emitted light’s energy equals the energy difference between the shells.
• Line spectra: transitions from excited states produce discrete (line) spectra because emitted light energies are quantized.

Limitations for Multi-Electron Atoms (e.g., Helium)

• Bohr predicted emissions based only on shell-to-shell energy differences, but helium shows more spectral lines than hydrogen.
• Energy levels become more finely subdivided in higher shells, leading to:
  • more distinct transition energies
  • additional and overlapping spectral lines

Limitation About Electron Orbits

• Bohr assumed electrons move on fixed circular orbits, with no electrons between shells.
• The lecture argues there was no clear evidence that electrons could be at precise, measurable orbital positions/velocities at all times.

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2) Modern (Quantum Mechanical) Atomic Model: Orbitals and Probability

• The uncertainty principle is emphasized as the key reason electrons cannot be assigned exact positions and velocities simultaneously.
  • Measuring position with light affects the electron’s momentum (especially for particles as small as electrons).
  • Therefore, electrons cannot be described as moving along definite paths.

Orbitals Represent Probability Space

• Instead of an exact location, an orbital indicates the region where an electron is likely to be found.
• Electron probability is visualized using:
  • Point density plots: probability shown as a “cloud” of points with varying density.
  • Boundary plots: a boundary enclosing regions where the probability is ≥ 90% (as described).

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3) Shapes of Orbitals and Classification (S, P, D)

• Orbitals are not always perfect circles; they have different shapes and orientations:

  • S orbitals: spherical (described as not directional)
  • P orbitals: three orientations corresponding to the x, y, z axes
  • D orbitals: five orientations (a higher level of subdivision)

• The lecture links these orbital shapes to probability distributions and diagrams where electrons “appear” in different forms.

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4) Electron Capacity and the Shell/Orbital Relationship

• Capacity rule: up to 2 electrons per orbital.

Bohr Shells vs. Modern Orbitals

• First shell:
  • corresponds to 1s (S) orbital → max 2 electrons
• Second shell:
  • corresponds to 2s (S) plus 2p (P) orbitals
    • 2s holds 2 electrons
    • three 2p orbitals together hold up to 6 electrons
    • total up to 8 electrons (matching Bohr shell capacity)
• Third shell:
  • corresponds to 3s, 3p, 3d
    • S: 2 electrons
    • three P orbitals: 6 electrons
    • five D orbitals: up to 10 electrons
    • total up to 18 electrons

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5) Why Multi-Electron Atoms Have Richer Spectra Than Bohr Predicted

• Within orbitals, subdivision within shells (s, p, d) provides:
  • different energies
  • multiple orientations
  • more possible transitions
• Even if shell-to-shell energy differences exist, additional energy levels produce more emission lines than Bohr’s simpler model anticipates.

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6) Electron Configurations Using Quantum Numbers

Electron Configuration Notation

• Configuration notation shows orbital type and how many electrons occupy each orbital (e.g., 1s², 2s², 2p⁶, 3s², as described for magnesium-like filling).

Principal Quantum Number (n)

• Written as the leading number (e.g., 1s, 2s, 3s).
• Determines:
  • energy
  • orbital size
• Larger n → higher energy and a larger probability region.

Azimuthal Quantum Number (l)

• Determines orbital shape.
• Mapping described in the lecture:
  • s orbital: (l = 0)
  • p orbital: (l = 1)
  • d orbital: (l = 2)
• Energy also depends on l when n is the same (higher (l) generally implies higher energy in the described framework).

Magnetic Quantum Number (mₗ)

• Determines the orientation of the orbital in space.
• Rules described:
  • For s (l = 0): (m_l = 0)
  • For p (l = 1): (m_l) ranges −1, 0, +1
  • For d (l = 2): (m_l) ranges −2 to +2

Pattern Summary

• If the principal quantum number is n, then:
  • the azimuthal quantum number l runs up to n − 1.

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Methodology / “How-To” Style Representation (As Described)

Represent Electron Probability

• Measure the probability of finding an electron.
• Create:
  • a point density plot (points with varying density)
  • a boundary plot enclosing regions where probability is ≥ 90%

Build Electron Configurations

• Use orbital symbols (s, p, d) and electron counts per orbital.
• Fill orbitals in order of lowest energy first (as stated).
• Enforce:
  • max 2 electrons per orbital

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Researchers or Sources Featured

• Niels Bohr (Bohr’s atomic model; limitations discussed)
• Uncertainty principle (conceptual source referenced, indirectly; specific person not named in the subtitles)