Loading learn tools
Loading topics
Loading home…Bohr’s model successfully explained the line spectrum of hydrogen by introducing quantized energy levels. It showed that electrons revolve in allowed orbits without radiating energy continuously. Energy is absorbed or emitted only when an electron jumps between levels. The model introduced the idea of discrete spectral lines matching Rydberg’s formula for hydrogen. It also linked atomic structure to the Planck quantum idea. Although it failed for multi-electron atoms and could not explain fine structure, it was a crucial bridge from Rutherford’s nuclear atom to quantum mechanics. Modern orbital models keep the idea of quantized energy that Bohr first made useful for chemistry.
A proton has charge +1.6×10⁻¹⁹ C and a relative mass of about 1 u. A neutron is electrically neutral and has a relative mass nearly equal to the proton (slightly larger). An electron has charge −1.6×10⁻¹⁹ C and a very small mass (about 11836 of a proton). Most of an atom’s mass therefore lies in the nucleus. Chemical behaviour is dominated by electrons because they occupy the outer regions and take part in bonding. Nuclear charge equals the number of protons and defines the element.
Across a period, atomic radius generally decreases because nuclear charge increases while electrons are added to the same shell. Greater attraction pulls the electron cloud closer. Down a group, atomic radius increases because a new shell is added. Although nuclear charge also increases, the extra shell and shielding dominate, so size grows. Noble gases are often compared carefully because of how radius is defined. These trends help predict ion sizes and lattice properties.
Shielding is the reduction of the full nuclear attraction felt by outer electrons due to inner electrons. Inner shells partially cancel the pull of the nucleus on valence electrons. Greater shielding makes valence electrons easier to remove, lowering ionization energy. Shielding increases down a group as more inner shells are present. Across a period, shielding changes less because electrons enter the same principal shell. Understanding shielding explains many periodic trends.
A cation forms when electrons are removed, often emptying the outer shell, so remaining electrons are held more tightly by the same nuclear charge. Electron–electron repulsion also decreases. An anion forms when electrons are added, increasing repulsion among electrons while nuclear charge stays the same. The electron cloud expands, so anions are larger than the parent atoms. For isoelectronic species, higher nuclear charge gives smaller radius. These ideas are essential for ionic lattice comparisons.
The magnetic quantum number mℓ specifies the orientation of an orbital in space. For a given ℓ, mℓ takes integer values from −ℓ to +ℓ, including zero. For s orbitals (ℓ=0), mℓ = 0 only. For p orbitals (ℓ=1), mℓ = −1, 0, +1 (three orientations). For d orbitals (ℓ=2), five values exist. In a magnetic field, these orientations can differ slightly in energy (Zeeman effect at advanced level). Together with n, ℓ and ms, mℓ uniquely labels an electron’s quantum state.
No. Pauli’s exclusion principle states that no two electrons in an atom can have the same set of four quantum numbers. An orbital is fixed by n, ℓ and mℓ, so the two electrons in it must differ in spin quantum number ms (+½ and −½). Therefore paired electrons in one orbital always have opposite spins. Same-spin electrons cannot occupy the same orbital. This rule shapes electron configurations and spectroscopic terms.
In building up neutral atoms, the 4s orbital is slightly lower in energy than 3d for early transition elements, so electrons enter 4s before 3d (Aufbau). Once 3d begins to fill, orbital energies rearrange. In ions, 3d becomes lower than 4s, so transition metals typically lose 4s electrons before 3d electrons. That is why Fe is [Ar] 4s² 3d⁶ but Fe²⁺ is often written [Ar] 3d⁶. Remembering this order prevents common configuration mistakes.
Magnesium has configuration [Ne] 3s², so the first two ionizations remove the two valence 3s electrons. After Mg²⁺, the ion has a noble-gas core. Removing a third electron means breaking into a stable filled shell, which requires much more energy. Therefore IE₃ ≫ IE₂ for Mg. Such jumps reveal the number of valence electrons and confirm group number. Similar patterns appear for other s-block metals.
Semiconductors have electrical conductivity between conductors and insulators. Their valence and conduction bands are separated by a moderate energy gap. At low temperature few electrons jump the gap, so conductivity is low. Heating or doping increases charge carriers and conductivity rises. Silicon and germanium are classic elemental semiconductors. Impurity doping (n-type or p-type) is used in electronic devices. Chemistry links semiconductor behaviour to periodic position and bonding.
Quantum numbers completely specify the state of an electron in an atom.
1. Principal quantum number (n): positive integers 1, 2, 3, … naming shells K, L, M, ….
Larger n means higher energy and greater average distance from the nucleus.
Maximum electrons in a shell = 2n².
2. Azimuthal quantum number (ℓ): for a given n, ℓ = 0 to (n−1).
It labels subshells and orbital shapes: s (ℓ=0), p (1), d (2), f (3).
In multi-electron atoms, energy depends on both n and ℓ.
3. Magnetic quantum number (mℓ): values −ℓ … 0 … +ℓ.
It gives 2ℓ+1 orbitals in a subshell and their orientation in space.
A magnetic field can split mℓ levels (Zeeman effect at advanced level).
4. Spin quantum number (ms): +½ or −½ for the two spin states.
Pauli’s exclusion principle: no two electrons share all four quantum numbers.
Therefore one orbital (fixed n, ℓ, mℓ) holds at most two opposite-spin electrons.
Example: a 2p electron has n=2, ℓ=1, mℓ = −1, 0 or +1, and ms = ±½.
These labels underpin electron configurations, magnetism and spectroscopy.
Exam answers should list allowed values and one physical meaning for each quantum number.
Together they replace Bohr’s single orbit number with a fuller quantum description.
Mass spectrometry separates ions by mass-to-charge ratio (mz).
Stage 1 — Vaporization: the sample becomes a gas.
Stage 2 — Ionization: electron impact removes electrons, forming positive ions.
Stage 3 — Acceleration: an electric field speeds ions through slits.
Stage 4 — Deflection: a magnetic field curves paths; lighter ions (smaller mz) deflect more.
Stage 5 — Detection: ions of selected mz produce a signal proportional to abundance.
Isotopes of one element share Z but differ in mass, so they appear as separate peaks.
Relative peak heights give percentage abundances.
Average atomic mass is the abundance-weighted mean of isotopic masses.
Classic school examples: Cl (35 and 37) and Mg (24, 25, 26).
The technique also identifies molecular ions and fragments in organic analysis.
Deflection depends on mz, not mass alone, so charge state matters.
Calibration with known standards improves accuracy.
Exam focus: name stages in order and link peak intensity to isotopic abundance.
State clearly why isotopes separate while chemical properties stay nearly identical.
Mass spectrometry thus connects atomic structure to measurable isotopic composition.
Electronic configurations follow Aufbau, Pauli and Hund rules.
Aufbau: electrons enter the lowest available orbitals first (1s, 2s, 2p, 3s, 3p, 4s, 3d, …).
The diagonal rule helps remember the fill order for neutral atoms.
Pauli: an orbital holds at most two electrons with opposite spins.
Helium 1s² is the simplest paired example.
Hund: degenerate orbitals fill singly with parallel spins before pairing.
Nitrogen 2p³ is ↑ ↑ ↑, minimizing repulsion and matching paramagnetism.
Exceptions: Cr and Cu prefer half-filled/fully filled d sets (4s¹ 3d⁵ and 4s¹ 3d¹⁰).
For transition-metal ions, remove 4s electrons before 3d electrons.
Condensed forms use noble-gas cores, e.g. Fe = [Ar] 4s² 3d⁶.
These rules predict valence, ion charges and unpaired-electron magnetism.
Spectra and periodic trends also rely on correct configurations.
Common errors: wrong 4s/3d order in ions and ignoring Hund’s rule.
Always count electrons to match atomic number or ion charge.
Write subshell notation carefully (superscripts) in exams.
Configuration skill is foundational for bonding and periodicity chapters.
Ionization energy (IE) is energy needed to remove 1 mol of electrons from 1 mol of gaseous atoms/ions.
Across a period, IE generally rises: nuclear charge increases while shell number stays similar.
Dips occur at Group IIA→IIIA (p electron after s²) and VA→VIA (pairing repulsion in p⁴).
Down a group, IE generally falls: larger radius and greater shielding weaken attraction.
Successive IE values always increase because each electron is removed from a more positive ion.
A large jump reveals that a noble-gas core has been reached.
Factors: nuclear charge, radius, shielding, subshell type and electron pairing.
Applications: metal reactivity, cation formation and confirming group number.
Example: Mg shows a big jump after IE₂ because Mg²⁺ is a neon core.
Compare IE trends with atomic radius trends (often inverse across a period).
Use kJ mol⁻¹ units and specify which electron is removed (IE₁, IE₂, …).
Plotting successive IE is a standard exam interpretation skill.
IE connects quantum shell structure to laboratory energetics.
Correct trend statements plus one anomaly explanation score highly.
Atomic emission spectroscopy (AES) identifies elements by light emitted from excited atoms.
Atoms are excited in a flame, arc, spark or plasma.
Electrons jump to higher levels, then return and emit photons of characteristic wavelengths.
Each element has a unique line spectrum — a fingerprint.
Line intensity relates to concentration for quantitative work.
Procedure idea: introduce sample → atomize/excite → disperse light → detect lines → compare standards.
Qualitative use: presence/absence of elements from characteristic lines.
Quantitative use: calibration curves of intensity versus concentration.
Applications: alloys, water analysis, foods, environmental monitoring.
Astronomy uses related emission/absorption line ideas for stellar composition.
Link to Bohr: ΔE = hν explains discrete lines from quantized levels.
Limitations: line overlap, matrix effects, need for careful calibration.
School answers should state principle, one instrument outline and two uses.
AES shows atomic structure theory working in practical chemical analysis.
It reinforces that electron transitions are quantized, not continuous.
Safety and proper sample preparation matter in real laboratories.
Mg (Z=12): 1s² 2s² 2p⁶ 3s². Mg²⁺ loses two electrons → 1s² 2s² 2p⁶ (10 electrons, neon core).
Cl (Z=17): 1s² 2s² 2p⁶ 3s² 3p⁵. Cl⁻ gains one electron → 1s² 2s² 2p⁶ 3s² 3p⁶ (18 electrons, argon configuration).
Final: Mg²⁺ has 10 e⁻; Cl⁻ has 18 e⁻.
Average atomic mass = Σ isotopic mass × abundance100
= 35×75 + 37×25100
= 2625 + 925100
= 3550100 = 35.5 u
Final Answer: 35.5 u
Average = 24×79 + 25×10 + 26×11100
= 1896 + 250 + 286100
= 2432100 = 24.32 u
Final Answer: 24.32 u
Al (Z=13): Al³⁺ has 13 protons and 10 electrons; config 1s² 2s² 2p⁶.
S (Z=16): S²⁻ has 16 protons and 18 electrons; config 1s² 2s² 2p⁶ 3s² 3p⁶.
Both are not isoelectronic with each other (10 vs 18 electrons). Al³⁺ is isoelectronic with Ne; S²⁻ with Ar.
Final: Al³⁺ (13p, 10e); S²⁻ (16p, 18e).
IE per mole = 496 kJ mol⁻¹ = 496 × 10³ J mol⁻¹
IE per atom = 496 × 10³NA
NA = 6.022 × 10²³ mol⁻¹
= 4960006.022×10²³ ≈ 8.24 × 10⁻¹⁹ J
Final Answer: ≈ 8.24 × 10⁻¹⁹ J per atom
Fe (Z=26): [Ar] 4s² 3d⁶
Fe³⁺: remove 4s² then one 3d → [Ar] 3d⁵
Cu (Z=29): exception → [Ar] 4s¹ 3d¹⁰ (not 4s² 3d⁹)
Final: Fe [Ar] 4s² 3d⁶; Fe³⁺ [Ar] 3d⁵; Cu [Ar] 4s¹ 3d¹⁰
Look for the large jump in successive IE values.
IE₁ to IE₄ increase moderately; there is a very large jump from IE₄ (4356) to IE₅ (16091).
This means four valence electrons are relatively easy to remove; the fifth comes from a stable inner shell.
Therefore the element is in Group IV (Group 14).
Final Answer: Group IV / Group 14