Structure of Atom: Particles, Bohr Model, Quantum Numbers and Orbitals
A from-scratch guide to the atom for CBSE Class 11 Science: the three sub-atomic particles, atomic and mass number, the Bohr model with a worked numerical, the four quantum numbers, orbitals, and the Aufbau, Pauli and Hund rules for electronic configuration - with the Cr and Cu exceptions.
By the PadhoDost Team · 📖 8 min read · Updated 4 August 2026
Part of Class 11 (CBSE) prep🧠 Think of the atom as a housing society
Picture an atom as a tall housing society, dost. Right at the centre is a tiny but super-heavy manager's office called the nucleus, packed with protons and neutrons. The electrons are the residents living on floors all around it. Each floor (shell) has flats (subshells), and each flat has rooms (orbitals) - and every room can hold at most two residents, who must sit facing opposite ways. Hold on to this picture: the whole chapter is really just the rules of who lives where.
Meet the three residents: electron, proton and neutron
Every atom is built from three sub-atomic particles. Electrons (discovered by J. J. Thomson from cathode rays) carry a negative charge and are extremely light. Protons (identified from Goldstein's anode or canal rays, and named by Rutherford) carry an equal but positive charge and are about 1836 times heavier than an electron. Neutrons (discovered by James Chadwick) have almost the same mass as a proton but carry no charge. Protons and neutrons sit tightly together in the nucleus, while electrons move in the space around it.
| Particle | Symbol | Relative charge | Approx. mass (u) | Discovered by |
|---|---|---|---|---|
| Electron | e- | -1 | 0.00055 (about 1/1836) | J. J. Thomson |
| Proton | p+ | +1 | 1.007 (about 1) | Goldstein / Rutherford |
| Neutron | n0 | 0 | 1.008 (about 1) | James Chadwick |
Bohr's model: electrons run on fixed tracks
In 1913 Niels Bohr pictured the electron of a hydrogen atom moving in fixed circular paths called orbits or stationary states. His key ideas were: (1) an electron can stay only in certain allowed orbits and does NOT lose energy while circling in them; (2) the angular momentum of the electron is quantised - it can only be a whole-number multiple of h/2 pi; and (3) energy is absorbed when an electron jumps to a higher orbit and emitted as light when it falls to a lower one, with the energy gap equal to Planck's constant times the frequency (delta-E = h nu). This model beautifully explained the line spectrum of hydrogen.
📝 Radius and energy of the electron in the n = 2 orbit of hydrogen
Find the radius and energy of the electron in the n = 2 orbit of a hydrogen atom (Z = 1).
Radius: r(n) = 0.529 x n^2 angstrom = 0.529 x (2)^2 = 0.529 x 4
r(2) = 2.116 angstrom = 211.6 pm
Energy: E(n) = -13.6/n^2 eV = -13.6/(2)^2 = -13.6/4
E(2) = -3.4 eV. In joules: -3.4 x 1.602 x 10^-19 = -5.45 x 10^-19 J (same as -2.18 x 10^-18 / 4).
The negative sign means the electron is bound to the nucleus; energy is lowest (most negative, -13.6 eV) in n = 1, the ground state.
Quantum numbers: the exact address of an electron
The four quantum numbers
- ✓Principal (n): the shell or floor. n = 1, 2, 3, ... It decides the size and main energy of the orbit; a shell can hold up to 2n^2 electrons.
- ✓Azimuthal (l): the subshell or shape. l ranges from 0 to (n-1). Values l = 0, 1, 2, 3 mean s, p, d, f subshells.
- ✓Magnetic (m_l): the orientation of an orbital in space. It takes (2l+1) values, from -l to +l including 0.
- ✓Spin (m_s): the direction of the electron's spin, either +1/2 (up-arrow) or -1/2 (down-arrow).
| Subshell | l value | Orbitals (2l+1) | Max electrons (2 x orbitals) |
|---|---|---|---|
| s | 0 | 1 | 2 |
| p | 1 | 3 | 6 |
| d | 2 | 5 | 10 |
| f | 3 | 7 | 14 |
Filling the rooms: Aufbau, Pauli and Hund
Three rules for placing electrons
- 1Aufbau principle: fill orbitals from lowest energy to highest. Use the (n + l) rule - the subshell with the smaller (n + l) fills first; if two are equal, the one with the smaller n fills first. Order: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, ...
- 2Pauli exclusion principle: no two electrons in an atom can have all four quantum numbers the same. So one orbital holds at most 2 electrons, and they must have opposite spins (up and down).
- 3Hund's rule of maximum multiplicity: within a set of equal-energy (degenerate) orbitals, electrons occupy them singly with parallel spins first; pairing begins only after each orbital has one electron.
📝 Electronic configuration of iron (Z = 26)
Iron has Z = 26, so a neutral atom has 26 electrons to place.
Fill by increasing energy (Aufbau, n+l rule): 1s -> 2s -> 2p -> 3s -> 3p -> 4s -> 3d ...
1s2 2s2 2p6 3s2 3p6 = 18 electrons (this is the argon core, [Ar]).
Next: 4s2 takes the count to 20, then 3d6 takes it to 26.
Configuration: 1s2 2s2 2p6 3s2 3p6 3d6 4s2 = [Ar] 3d6 4s2
In 3d6, the five d-orbitals first take one electron each (Hund), then the sixth pairs up -> giving 4 unpaired electrons.
Quick revision
- ✓An atom = nucleus (protons + neutrons) + electrons around it; Z = protons, A = protons + neutrons; same Z different A = isotopes.
- ✓Bohr model: fixed orbits with quantised energy; for hydrogen E(n) = -13.6/n^2 eV and r(n) = 0.529 n^2 angstrom.
- ✓Four quantum numbers (n, l, m_l, m_s) fix each electron's address; no two electrons share all four (Pauli).
- ✓Fill order follows Aufbau (n+l rule); degenerate orbitals fill singly first (Hund) before pairing.
- ✓Remember the chromium and copper exceptions for extra-stable half-filled and fully-filled d subshells.
⚡ Quick check
Following Hund's rule, how many unpaired electrons are present in a nitrogen atom (Z = 7)?
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