How Are Electrons Distributed in an Atom?

Electron Shells: K, L, M, N, O, P, Q Notation

Origin and Principle

To describe the distribution of electrons around the atomic nucleus, physicists use a simple historical notation: the electron shells K, L, M, N, O, P, and Q. This notation was introduced in the early 20th century by physicist Charles Barkla (1877-1944) during the study of X-rays. This notation allows for a quick visualization of how electrons are distributed by increasing energy levels, from the shell closest to the nucleus (K) to the outer shells.

Correspondence with Modern Notation

Each letter corresponds to a principal quantum number n:
K Shell: n = 1 (first shell, closest to the nucleus)
L Shell: n = 2 (second shell)
M Shell: n = 3 (third shell)
N Shell: n = 4 (fourth shell)
O Shell: n = 5 (fifth shell)
P Shell: n = 6 (sixth shell)
Q Shell: n = 7 (seventh shell)

Maximum Capacity of Shells

Each shell can contain a maximum number of electrons defined by the formula 2n²:
K Shell (n=1): maximum 2 electrons (2 × 1² = 2)
L Shell (n=2): maximum 8 electrons (2 × 2² = 8)
M Shell (n=3): maximum 18 electrons (2 × 3² = 18)
N Shell (n=4): maximum 32 electrons (2 × 4² = 32) → Uranium reaches this: K(2) L(8) M(18) N(32)
O Shell (n=5): maximum 50 electrons (2 × 5² = 50) → Never reached (uranium has only 21 electrons in O)
P Shell (n=6): maximum 72 electrons (2 × 6² = 72) → Never reached
Q Shell (n=7): maximum 98 electrons (2 × 7² = 98) → Never reached

N.B.:
In practice, no known element completely fills the shells beyond N. The heaviest natural element, uranium (Z=92), has the configuration K(2) L(8) M(18) N(32) O(21) P(9) Q(2). The heaviest confirmed synthetic element, oganesson (Z=118), has the configuration K(2) L(8) M(18) N(32) O(32) P(18) Q(8).

Internal Structure of Shells: Subshells

Each shell is divided into subshells designated by the letters s, p, d, f:
s Subshell: can contain up to 2 electrons (1 orbital)
p Subshell: can contain up to 6 electrons (3 orbitals)
d Subshell: can contain up to 10 electrons (5 orbitals)
f Subshell: can contain up to 14 electrons (7 orbitals)

K Shell (n=1): contains only 1s (2 electrons max)
L Shell (n=2): contains 2s and 2p (2 + 6 = 8 electrons max)
M Shell (n=3): contains 3s, 3p, and 3d (2 + 6 + 10 = 18 electrons max)
N Shell (n=4): contains 4s, 4p, 4d, and 4f (2 + 6 + 10 + 14 = 32 electrons max)
O Shell (n=5): contains 5s, 5p, 5d, and 5f (2 + 6 + 10 + 14 = 32 electrons max theoretical, although the theoretical 5g subshell does not exist in known elements)
P Shell (n=6): contains 6s, 6p, 6d, and 6f (2 + 6 + 10 + 14 = 32 electrons max for known subshells)
Q Shell (n=7): contains 7s, 7p, and potentially 7d (only 7s and 7p electrons are observed in known elements)

Simplified Notation K(x) L(y) M(z) N(t)

This notation indicates the total number of electrons present in each shell, without detailing the subshells. It is particularly useful for quickly visualizing the overall electronic distribution of an atom.

Examples of Elements

Helium (2 electrons): 1s² → K(2)
The K shell is complete and saturated.
Neon (10 electrons): 1s² 2s² 2p⁶ → K(2) L(8)
The K and L shells are complete and saturated.
Sodium (11 electrons): 1s² 2s² 2p⁶ 3s¹ → K(2) L(8) M(1)
The K and L shells are complete, the M shell contains only 1 electron out of 18 possible.
Argon (18 electrons): 1s² 2s² 2p⁶ 3s² 3p⁶ → K(2) L(8) M(8)
The K and L shells are complete. The M shell contains 8 electrons but is not complete (the 3s and 3p subshells are saturated, but 3d remains empty).
Calcium (20 electrons): 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² → K(2) L(8) M(8) N(2)
Note that the 4s subshell fills before the 3d, which is why the M shell remains at 8 electrons.
Titanium (22 electrons): 1s² 2s² 2p⁶ 3s² 3p⁶ 3d² 4s² → K(2) L(8) M(10) N(2)
The M shell begins to fill with 3d electrons.

Order of Filling Shells

The filling order does not strictly follow the order of K, L, M, N shells… due to the energy levels of the subshells. The general order is:
1s → 2s → 2p → 3s → 3p → 4s → 3d → 4p → 5s → 4d → 5p → 6s → 4f → 5d → 6p → 7s → 5f → 6d…

This principle explains why, for example, potassium (19 electrons) has the configuration K(2) L(8) M(8) N(1): the 19th electron goes into 4s rather than 3d because the 4s subshell is of lower energy than 3d.

Importance of This Notation

The K, L, M, N, O, P, Q notation allows:
• Quick visualization of the overall electronic structure of an atom
• Easy identification of the valence shell (outer shell)
• Understanding of chemical properties related to valence electrons
• Explanation of the classification of elements in the periodic table
• Prediction of oxidation states and chemical reactivity of elements

Examples:

• Bromine: The notation K(2) L(8) M(18) N(7) immediately shows that bromine has 7 electrons in its outer shell, without having to decipher the long configuration 1s² 2s² 2p⁶ 3s² 3p⁶ 3d¹⁰ 4s² 4p⁵.
• Iron: Similarly, iron (Z = 26) with its configuration 1s² 2s² 2p⁶ 3s² 3p⁶ 3d⁶ 4s² is summarized as K(2) L(8) M(14) N(2), clearly showing that its 8 valence electrons (6 in 3d and 2 in 4s) explain its multiple oxidation states (+2 and +3).
• Zinc: Zinc (Z = 30) with its configuration 1s² 2s² 2p⁶ 3s² 3p⁶ 3d¹⁰ 4s² becomes simply K(2) L(8) M(18) N(2), instantly revealing that its 3d subshell is complete and that only the 2 electrons in 4s participate in reactions, hence its unique oxidation state +2.

Electronic Structure and Chemical Affinities of Elements

The chemical reactivity of elements originates from their electronic structure, particularly the configuration of their valence shell. The outer shell, or valence shell, determines an element's ability to form chemical bonds: atoms tend to gain, lose, or share electrons to achieve a stable configuration, usually that of the nearest noble gas.

This tendency explains the observed chemical affinities: alkali metals, with a single valence electron, readily give it up to form cations; halogens, which lack one electron to complete their outer shell, are electron-hungry and form anions; while noble gases, with a complete valence shell, remain chemically inert. Between these extremes, transition elements and metalloids exhibit intermediate behaviors, forming various types of bonds depending on conditions.

Understanding these structure-property relationships is the foundation of modern chemistry and allows the prediction of element behavior in chemical reactions.