Inside the atom: from experiments to orbitals.
Understand how electrons, nuclei, spectra and quantum numbers fit together — and why Bohr’s neat circles are not the complete modern picture.
Why this chapter matters
UPSC-style general-science items may combine a basic discovery, an atomic-number calculation and a statement about modern electron arrangement. Learning the experiments first makes the rules of orbitals and electronic configuration more intuitive.
Separate experimentally established particles from models used to explain them. In every ion problem, count protons from atomic number, neutrons from mass number, and electrons from charge.
The path to the modern atomic model
Dalton’s early atomic theory helped explain chemical combination, but it treated atoms as indivisible; discovery of subatomic particles and isotopes required revision. J. J. Thomson’s cathode-ray work established the electron’s charge-to-mass ratio and contributed to the discovery of the electron. Millikan’s oil-drop experiment measured the magnitude of the elementary charge.
| Experiment / scientist | What it established | Important limitation |
|---|---|---|
| Cathode rays / J. J. Thomson | Negatively charged particles (electrons); e/m ratio | Did not yield a complete nuclear picture. |
| Oil-drop / R. A. Millikan | Elementary electric charge magnitude | Not a direct experiment measuring nuclear size. |
| Gold-foil scattering / E. Rutherford and colleagues | A tiny, concentrated, positively charged nucleus; atom mostly empty space | Classical planetary orbits could not account for atomic stability and spectra. |
| Neutron discovery / J. Chadwick | Electrically neutral nuclear particle, neutron | Neutron is not responsible for atomic number. |
Rutherford’s key evidence was that most alpha particles passed through the thin foil, but a small fraction scattered at large angles. If positive charge had been uniformly distributed throughout the atom, the latter observation would have been hard to explain.
Atomic number, mass number, ions and isotopes
Atomic number (Z) equals the number of protons and defines the element. Mass number (A) counts protons plus neutrons in one nucleus. For a neutral atom, the electron count equals Z. In a cation electrons have been lost; in an anion electrons have been gained. Ordinary chemical ion formation changes electrons, not the number of protons.
| Species | Protons | Neutrons | Electrons |
|---|---|---|---|
| ²³Na atom (Z=11) | 11 | 12 | 11 |
| ²³Na⁺ ion | 11 | 12 | 10 |
| ³⁵Cl⁻ ion (Z=17) | 17 | 18 | 18 |
| ⁴⁰Ca²⁺ ion (Z=20) | 20 | 20 | 18 |
Isotopes have the same Z but different A (for example ¹²C and ¹⁴C). Isobars have the same A but different Z (for example ⁴⁰Ar and ⁴⁰Ca). Isotones have equal numbers of neutrons but different proton numbers. Isoelectronic species have equal numbers of electrons, even if their nuclei differ.
Isotopes belong to the same element; isobars need not. Na⁺ and Ne both have 10 electrons, but are not isotopes.
Why periodic-table atomic masses are often decimals
Most elements occur naturally as mixtures of isotopes. Their tabulated standard atomic weights reflect isotopic abundances and masses, so they need not be integers. A simplified numerical example uses an element with 75% of isotope mass 35 u and 25% of isotope mass 37 u.
Isotope masses themselves are not always exactly equal to mass numbers expressed in u. In exam arithmetic, the problem may explicitly provide rounded mass numbers or relative abundances; use those values rather than substituting an unrelated atomic weight.
Electromagnetic radiation, photons and atomic spectra
Electromagnetic radiation is described by wavelength λ, frequency ν and speed c in vacuum. Shorter wavelength means higher frequency and photon energy. Planck’s equation assigns photon energy in discrete quanta, E = hν. The visible spectrum is a relatively small part of the electromagnetic spectrum.
| Radiation order (higher frequency → lower frequency) | Useful fact |
|---|---|
| Gamma → X-ray → ultraviolet → visible → infrared → microwave → radio | Photon energy decreases from left to right; wavelength increases. |
| Photoelectric emission | Requires photon frequency above the metal’s threshold; increasing intensity alone cannot overcome sub-threshold frequency. |
An excited atom emits radiation at characteristic wavelengths when electrons make transitions between allowed energy levels. This produces a line spectrum, rather than a continuous band covering every wavelength.
Bohr’s model and hydrogen spectral series
Bohr proposed allowed stationary energy levels for the hydrogen atom. Light is absorbed or emitted when an electron changes energy level; the photon energy equals the difference between the levels. The model successfully accounts for much of the hydrogen spectrum but does not fully describe multi-electron atoms or modern orbital probability distributions.
| Spectral series | Final level n | Region |
|---|---|---|
| Lyman | 1 | Ultraviolet |
| Balmer | 2 | Mostly visible (series limit in near ultraviolet) |
| Paschen | 3 | Infrared |
| Brackett | 4 | Infrared |
When an electron falls from a higher energy level to a lower one, energy is emitted. When it absorbs an appropriately energetic photon, it can move to a higher level. An electron’s position is not a tiny planet following a precise circular path in the quantum-mechanical account.
Bohr’s fixed-radius orbits are historically important, but a modern atomic orbital is a probability-related description from quantum mechanics, not the same thing as an orbit.
Quantum numbers and the meaning of orbitals
Quantum mechanics describes electron states with four quantum numbers. The principal number n gives shell and energy/size information; the azimuthal number l specifies subshell type; the magnetic number ml labels orbitals within a subshell; and spin ms distinguishes two allowed spin projections.
| Number | Allowed values | What to remember |
|---|---|---|
| n | 1, 2, 3, … | Principal shell; maximum electrons per shell = 2n². |
| l | 0 to n−1 | 0=s, 1=p, 2=d, 3=f. |
| mₗ | −l through +l | Number of orbitals in a subshell = 2l+1. |
| mₛ | +½ or −½ | Each orbital can hold at most two electrons with opposite spins. |
1 orbital; maximum 2 electrons.
3 orbitals; maximum 6 electrons.
5 orbitals; maximum 10 electrons.
7 orbitals; maximum 14 electrons.
For n = 2, l may be 0 or 1 only. A d subshell requires l = 2 and therefore n ≥ 3.
Aufbau principle, Pauli exclusion and Hund’s rule
Electron configuration assigns electrons to orbitals. In the Aufbau scheme, lower-energy orbitals fill first for the ground state, with the (n+l) guideline helping determine the usual order. Pauli exclusion prevents two electrons in one atom from sharing all four quantum numbers. Hund’s rule directs electrons to occupy degenerate orbitals singly with parallel spins before pairing, for a typical ground-state arrangement.
| Element | Z | Ground-state electron configuration |
|---|---|---|
| Carbon | 6 | 1s² 2s² 2p² |
| Neon | 10 | 1s² 2s² 2p⁶ |
| Sodium | 11 | 1s² 2s² 2p⁶ 3s¹ |
| Chlorine | 17 | 1s² 2s² 2p⁶ 3s² 3p⁵ |
| Argon | 18 | 1s² 2s² 2p⁶ 3s² 3p⁶ |
Some transition-metal neutral atoms depart from a simple mechanical filling prediction: chromium is approximately [Ar] 3d⁵4s¹ and copper [Ar] 3d¹⁰4s¹. These special configurations are frequently used to test whether candidates merely memorised a sequence.
Two solved methods for particle-count and orbital questions
Example A: Count subatomic particles
Example B: Capacity of the n = 3 shell
For n = 3, allowed l values are 0 (3s), 1 (3p) and 2 (3d). Together there are 1 + 3 + 5 = 9 orbitals, allowing up to 18 electrons. This is the shell’s maximum capacity, not a claim that every atom fills its third shell completely before any fourth-shell orbital begins to fill.
Z determines identity; A−Z gives neutrons; charge adjusts electron count. For orbitals, write allowed n and l before assigning capacity.
One-minute recall sheet
- Z = number of protons; A = protons + neutrons; ion charge changes electron number.
- Isotopes: same Z, different A. Isobars: same A, different Z.
- Photon energy E = hν; shorter wavelength means greater photon energy.
- Bohr model explains hydrogen-like spectra; a modern orbital is not a fixed trajectory.
- For shell n, l = 0 to n−1; orbitals in a subshell = 2l+1; capacity = 2(2l+1).
- Pauli: two electrons per orbital with opposite spins; Hund: single occupation before pairing in degenerate orbitals.
- Neutral Cr and Cu exhibit familiar configurations [Ar]3d⁵4s¹ and [Ar]3d¹⁰4s¹.
The 2n² shell formula gives maximum capacity, not the simple chronological filling pattern in every element. Do not treat a Rutherford orbit, a Bohr orbit and a quantum orbital as synonyms.
UPSC-style practice — 15 explained questions
These are original practice questions, not claims of verbatim UPSC previous-year questions. Attempt each before opening the answer. Questions are single-correct unless specified.
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Answer: B. Large-angle alpha scattering required a concentrated positive centre, not a diffuse positive sphere.
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Answer: A. Protons=11, neutrons=23−11=12, electrons=11−1=10.
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Answer: C. Same Z defines the element; isotope variation is in neutron number and thus usually A.
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Answer: B. Na⁺ has 10 electrons and neutral neon also has 10.
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Answer: C. 0.75×35 + 0.25×37 = 35.5 u.
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Answer: B. Photon energy E=hc/λ, so it is inversely proportional to λ.
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Answer: D. The Lyman series ends at n=1 and lies in ultraviolet wavelengths.
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Answer: C. A 2d subshell would need n=2, l=2, but for n=2 only l=0,1 are possible.
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Answer: B. For l=2, 2l+1=5 orbitals; each holds at most 2 electrons.
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Answer: C. There are 3 p orbitals and 2 electron slots in each, yielding 6.
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Answer: D. Pauli exclusion concerns uniqueness of the full quantum state.
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Answer: B. After neon core 1s²2s²2p⁶, the 11th electron occupies 3s.
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Answer: A. The 3+ cation has lost three electrons from the neutral 13-electron atom.
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Answer: B. Moving to a lower-energy level releases a photon; n=3→2 is a Balmer transition.
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Answer: C. Neutral Cu has the experimentally favoured [Ar]3d¹⁰4s¹ arrangement.
Primary references and revision links
- NCERT official Chemistry textbook portal — Class XI (foundational concepts and chapter exercises).
- NCERT Exemplar Problems (additional concept practice).
- UPSC official previous question papers (check actual wording and level for your exam).
- CrackTarget: 500 One-liner Chemistry Concepts for UPSC (quick revision).
- CrackTarget Science Resource Directory (related science topics).
Chapter explanations and practice questions are prepared for general-science revision. Topic coverage and depth differ by examination and official syllabus.