Exhaustive Study Notes on Electron Shells, Atomic Structure, Excitation, and Ionisation

Atomic Shell Structure and the 2n² Capacity Rule

• Electron shells represent defined principal energy levels surrounding an atomic nucleus, designated by principal quantum numbers ($n$) and letter names:

  • K-shell: $n = 1$

  • L-shell: $n = 2$

  • M-shell: $n = 3$

  • N-shell: $n = 4$

  • O-shell: $n = 5$

• The maximum electron capacity of any principal shell is governed by the mathematical formula:   $\text{Maximum electron capacity} = 2n^2$

• Shell-by-shell electron capacity calculations:

  • K-shell ($n = 1$): $2 \times 1^2 = 2$ maximum electrons

  • L-shell ($n = 2$): $2 \times 2^2 = 8$ maximum electrons

  • M-shell ($n = 3$): $2 \times 3^2 = 18$ maximum electrons

  • N-shell ($n = 4$): $2 \times 4^2 = 32$ maximum electrons

  • O-shell ($n = 5$): $2 \times 5^2 = 50$ maximum electrons

Subshells and Orbital Filling Sequences

• Principal energy shells are subdivided into smaller subshells designated as $s$, $p$, $d$, and $f$:

  • $s$ subshell: contains 1 orbital, holds up to 2 electrons

  • $p$ subshell: contains 3 orbitals, holds up to 6 electrons

  • $d$ subshell: contains 5 orbitals, holds up to 10 electrons

  • $f$ subshell: contains 7 orbitals, holds up to 14 electrons

• Subshell composition within principal energy shells:

  • M-shell ($n = 3$): holds up to 18 electrons total across $s$, $p$, and $d$ subshells ($3s$, $3p$, $3d$)

  • N-shell ($n = 4$): holds up to 32 electrons total across $s$, $p$, $d$, and $f$ subshells ($4s$, $4p$, $4d$, $4f$)

• The Aufbau Principle dictates that electrons occupy energy subshells in order of increasing energy, filling the lowest available energy levels before occupying higher energy levels.

• Subshell filling order by increasing energy:

  • $1s$: K-shell ($n = 1$), lowest energy level, holds 2 electrons

  • $2s$: L-shell ($n = 2$), holds 2 electrons

  • $2p$: L-shell ($n = 2$), holds 6 electrons

  • $3s$: M-shell ($n = 3$), holds 2 electrons

  • $3p$: M-shell ($n = 3$), holds 6 electrons

  • $4s$: N-shell ($n = 4$), holds 2 electrons (fills prior to $3d$ due to lower energy state)

  • $3d$: M-shell ($n = 3$), holds 10 electrons

  • $4p$: N-shell ($n = 4$), holds 6 electrons

  • $5s$: holds 2 electrons

  • $4d$: holds 10 electrons

  • $5p$: holds 6 electrons

  • $6s$: holds 2 electrons

  • $5d$: holds 10 electrons

  • $4f$: holds 14 electrons

• A shell is defined as full when all of its available lower-energy orbitals ($s$, $p$, and sometimes $d$) are completely occupied by electrons. Once occupied, additional electrons enter the next subshell level.

Calcium Electron Configuration and Shell Occupation

• Calcium (chemical symbol $\text{Ca}$) has an atomic number of 20, containing 20 protons and 20 electrons.

• Detailed shell-by-shell and subshell electron distribution for Calcium:

  • K-shell ($n = 1$): $1s^2$ (2 electrons)

  • L-shell ($n = 2$): $2s^2 2p^6$ (8 electrons)

  • M-shell ($n = 3$): $3s^2 3p^6$ (8 electrons)

  • N-shell ($n = 4$): $4s^2$ (2 electrons)

• Reason Calcium utilizes 4 shells:

  • Although the M-shell ($n = 3$) has a maximum capacity of 18 electrons ($2n^2 = 2 \times 3^2 = 18$), the $3d$ subshell possesses a higher energy level than the $4s$ subshell.

  • Because electrons occupy the lowest available energy levels first, the $4s$ subshell fills with 2 electrons after $3s$ and $3p$ are filled, occupying the N-shell before any electrons enter the $3d$ orbital.

Reactivity Analysis of Elements

• Detailed electron structure of selected elements:

  • Potassium ($\text{K}$, Atomic Number 19): 19 protons, 19 electrons. Electron configuration: $2, 8, 8, 1$ ($1s^2 2s^2 2p^6 3s^2 3p^6 4s^1$). Contains 1 outer valence electron in the $4s$ subshell.

  • Magnesium ($\text{Mg}$, Atomic Number 12): 12 protons, 12 electrons. Electron configuration: $2, 8, 2$ ($1s^2 2s^2 2p^6 3s^2$). Contains 2 outer valence electrons in the $3s$ subshell.

  • Krypton ($\text{Kr}$, Atomic Number 36): 36 protons, 36 electrons. Electron configuration: $2, 8, 18, 8$ ($1s^2 2s^2 2p^6 3s^2 3p^6 3d^{10} 4s^2 4p^6$). Features a full outer octet in the $4s$ and $4p$ subshells.

• Reactivity ranking from MOST reactive to LEAST reactive:

  • Rank 1 (Most Reactive): Potassium ($\text{K}$, 19) — easily loses its single outer $4s$ valence electron due to weak nuclear attraction at a larger atomic radius.

  • Rank 2: Magnesium ($\text{Mg}$, 12) — moderately reactive, losing its 2 valence electrons ($3s^2$) during reactions.

  • Rank 3 (Least Reactive): Krypton ($\text{Kr}$, 36) — highly stable noble gas with a complete valence shell octet, resisting electron gain, loss, or sharing.

Nuclear Charge and Electron Binding Energies

• Electron binding energy is the energy required to remove an electron from a specific shell of an atom. It depends directly on atomic nuclear charge (number of protons) and distance from the nucleus.

• Comparison of Binding Energies in Barium ($\text{Ba}$, Atomic Number 56, Mass Number 137) and Tungsten ($\text{W}$, Atomic Number 74, Mass Number 184):

  • Barium ($\text{Ba-137}$, $Z = 56$):

  • K-shell ($n = 1$): 2 electrons, Binding Energy = $37\,\text{keV}$

  • L-shell ($n = 2$): 8 electrons, Binding Energy = $6\,\text{keV}$

  • M-shell ($n = 3$): 18 electrons, Binding Energy = $1.3\,\text{keV}$

  • N-shell ($n = 4$): 18 electrons, Binding Energy = $0.3\,\text{keV}$

  • O-shell ($n = 5$): 12 electrons, Binding Energy = $0.04\,\text{keV}$

  • P-shell ($n = 6$): 2 electrons

  • Tungsten ($\text{W-184}$, $Z = 74$):

  • K-shell ($n = 1$): 2 electrons, Binding Energy = $69\,\text{keV}$

  • L-shell ($n = 2$): 8 electrons, Binding Energy = $12\,\text{keV}$

  • M-shell ($n = 3$): 18 electrons, Binding Energy = $2.8\,\text{keV}$

  • N-shell ($n = 4$): 32 electrons, Binding Energy = $0.6\,\text{keV}$

  • O-shell ($n = 5$): 13 electrons, Binding Energy = $0.08\,\text{keV}$

  • P-shell ($n = 6$): 2 electrons

• Key physical principles governing binding energy:

  • Nuclear Charge ($Z$): Higher atomic numbers result in greater nuclear positive charge, exerting a stronger electrostatic pull on electrons and significantly increasing binding energies across corresponding shells (e.g., Tungsten K-shell binding energy is $69\,\text{keV}$ compared to Barium K-shell binding energy of $37\,\text{keV}$).

  • Distance from Nucleus: Binding energy decreases rapidly as shell level ($n$) increases ($K > L > M > N > O > P$) due to increased distance and electrostatic shielding from inner shell electrons.

Mechanisms of Electron Excitation

• Electron excitation is the process wherein an electron absorbs energy and moves from a lower energy level (ground state) to a higher energy level (excited state).

• Steps of electron excitation:

  • Ground State: Electron resides in its lowest, most stable energy configuration.

  • Energy Absorption: Energy is transferred to the electron.

  • Transition to Excited State: Electron jumps to a higher, vacant energy shell or orbital.

  • Unstable Excited State: The state is temporary; the electron eventually returns to the ground state, emitting surplus energy.

• Energy Quantization Rule: Energy absorbed by an electron must exactly match the energy gap between the initial energy level and the target energy level for excitation to take place.

• Energy sources capable of inducing electron excitation:

  • Electromagnetic Radiation (photons):

  • Visible light: supplies sufficient energy to excite outer valence electrons in specific atoms/molecules.

  • Ultraviolet (UV) light: carries higher energy capable of exciting outer or deeper shell electrons.

  • X-rays: high-energy photons that can excite inner-shell electrons depending on exact energy level.

  • Electrical Energy: Controlled electric fields (such as inside cathode ray tubes or specialized laboratory equipment) impart energy to excite electrons.

  • Thermal Energy: Heat transfers kinetic energy to excite outer-shell electrons in specific substances.

Ionisation Principles and Energetic Thresholds

• Ionisation is the process by which an atom or molecule loses or gains electrons, resulting in the formation of charged particles called ions.

• Energetic Threshold Requirement:

  • For ionisation to occur via electron removal, the transferred energy must be equal to or greater than the electron's binding energy ($\text{Energy Transferred} \ge \text{Binding Energy}$).

  • If transferred energy is less than the binding energy ($\text{Energy Transferred} < \text{Binding Energy}$), the electron cannot be ejected; it may undergo excitation if energy matches an orbital energy difference.

• Sequential steps of ionisation:

  • Ground State: Electrons exist in their stable configuration.

  • Energy Input: Energy absorbed from incoming particle or photon overcomes electrostatic attraction between electron and nucleus.

  • Electron Ejection: The electron is completely knocked off from the atomic shell.

  • Ion Formation:

  • Cation: Atom loses one or more electrons, acquiring a net positive charge (e.g., $\text{Na} \rightarrow \text{Na}^+ + e^-$).

  • Anion: Atom gains one or more electrons, acquiring a net negative charge (e.g., $\text{Cl} + e^- \rightarrow \text{Cl}^-$).

• Sources of Ionising Radiation:

  • Direct ionising charged particles: Alpha particles ($\alpha$), beta particles ($\beta$), and protons.

  • Indirectly ionising radiation: X-rays, gamma rays ($\gamma$), and neutrons.

  • Cosmic radiation: High-energy particle showers capable of direct and indirect ionisation.

Non-Ionising Energy Sources

• Non-ionising energy forms lack sufficient quantum energy to equal or exceed atomic binding energies, preventing them from ejecting electrons from atoms:

  • Solar radiation (visible light and infrared portions)

  • Radio waves

  • Microwaves

  • Infrared radiation

  • Visible light

  • Low-energy Ultraviolet (UV) light

  • Magnetic fields and magnetic energy

  • Bluetooth frequency signals

  • Wi-Fi signals

  • Gravitational energy

  • Sound waves and ultrasonic waves

  • Thermal energy / ambient heat

  • Chemical potential energy

The Electromagnetic Spectrum and Applications

• Electromagnetic radiation varies continuously across wavelengths and energy levels, categorized into specific region types:

• Key regions of the electromagnetic spectrum and their applications:

  • Radio waves: longest wavelengths; used to broadcast radio and television signals.

  • Microwaves: used in cooking, radar technology, telephone, and communication signals.

  • Infrared radiation: transmits heat from the sun, fires, and radiators.

  • Visible light: narrow band of electromagnetic spectrum that enables visual perception.

  • Ultraviolet (UV) radiation: absorbed by human skin; used in fluorescent light tubes.

  • X-rays: ionising high-energy radiation; used to view structural interiors of biological bodies and inanimate objects.

  • Gamma rays: highest energy ionising radiation; used in medical oncology for targeting and killing cancer cells.