Struktur Atom (6) | Bilangan Kuantum | utama, azimut, magnetik, spin

Summary

The video explains how to determine the four quantum numbers of an electron in an atom, usually focusing on the atom’s last electron. The presenter reviews each quantum number, then applies the rules to chlorine and fluorine.

The four quantum numbers

• Principal quantum number ((n))

  • Identifies the electron’s shell or energy level.
  • Read from the number before the subshell letter in an electron configuration. For example, in (3p), (n=3).
  • Possible shell values are (1) through (7).

• Azimuthal quantum number ((l))

  • Identifies the subshell.
  • The subshell-to-(l) mapping is:
    • (s \rightarrow 0)
    • (p \rightarrow 1)
    • (d \rightarrow 2)
    • (f \rightarrow 3)
  • The value of (l) must be less than (n).

• Magnetic quantum number ((m_l))

  • Identifies an orbital within a subshell.
  • Its possible values range from (-l) to (+l), including zero:
    • (s) ((l=0)): (m_l=0), one orbital
    • (p) ((l=1)): (m_l=-1, 0, +1), three orbitals
    • (d) ((l=2)): five values, from (-2) to (+2)
    • (f) ((l=3)): seven values, from (-3) to (+3)
  • Each orbital can hold at most two electrons.

• Spin quantum number ((m_s))

  • Represents the electron’s spin direction.
  • Its possible values are (+\tfrac12) and (-\tfrac12), commonly represented by opposite arrow directions in orbital diagrams.

Method for finding the quantum numbers of the last electron

1. Write the atom’s electron configuration.
2. Locate the last electron and read its shell number to determine (n).
3. Identify its subshell and use the (s,p,d,f) mapping to determine (l).
4. Determine the orbital containing the electron. Use the allowed (m_l) values from (-l) to (+l).
5. Determine the electron’s spin from its arrow direction in the orbital diagram.
6. When distributing electrons among orbitals in the same subshell, apply Hund’s rule: place one electron in each orbital before pairing electrons.

Examples

• Chlorine, (Z=17)

  • Electron configuration: (1s^2\,2s^2\,2p^6\,3s^2\,3p^5).
  • The last electron is in (3p), so (n=3) and (l=1).
  • The (p) subshell has three orbitals, with (m_l=-1, 0, +1). Applying Hund’s rule to the five (3p) electrons, the video assigns the last electron to the middle orbital, (m_l=0), with spin (m_s=-\tfrac12).
  • The resulting set is ((n,l,m_l,m_s)=(3,1,0,-\tfrac12)).

• Fluorine, (Z=9)

  • The video uses fluorine’s configuration, (1s^2\,2s^2\,2p^5), to assess which proposed quantum-number set is impossible.
  • It first checks whether the stated shell exists for fluorine’s electrons. A set with (n=3) is impossible because fluorine has no electrons in the third shell; the video identifies choice E.
  • More generally, check that (l<n), that (m_l) is between (-l) and (+l), and that (m_s) is either (+\tfrac12) or (-\tfrac12).

Speakers or sources featured

• One presenter/narrator from the Kimatika channel delivers the chemistry lesson.
• No other speakers or interviewees are featured.