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Atomic structure questions in JEE and NEET are rarely hard, but they are exact: one wrong value of mₗ, one misplaced electron, and the option is gone. The rules fit on half a page. This post sets them out, shows how to count orbitals and nodes without memorising tables, and covers the exceptions that examiners like.
What do the four quantum numbers tell you?
The NCERT Class 11 chapter on Structure of Atom defines them:
n, principal: 1, 2, 3 and so on. Sets the shell, and largely the size and energy.
l, azimuthal: 0 to n − 1. Sets the subshell and its shape: 0 is s, 1 is p, 2 is d, 3 is f.
mₗ, magnetic: −l to +l in whole steps, so 2l + 1 values. Sets the orbital's orientation.
mₛ, spin: +½ or −½.
Both the JEE (Main) 2026 syllabus and the NEET (UG)-2026 syllabus list the quantum numbers, the shapes of s, p and d orbitals, the aufbau principle, Pauli's exclusion principle, Hund's rule and the extra stability of half-filled and filled orbitals.
How do you count orbitals, electrons and nodes?
From the definitions, a subshell has 2l + 1 orbitals and a shell has n² orbitals, holding at most 2n² electrons.
Example 1. For n = 3: l can be 0, 1 or 2, giving 1 + 3 + 5 = 9 orbitals and 18 electrons.
Example 2. Which sets are allowed?
n = 2, l = 2: not allowed, since l can be at most n − 1 = 1.
n = 3, l = 1, mₗ = −2: not allowed, since mₗ runs only from −1 to +1.
n = 4, l = 3, mₗ = −3, mₛ = +½: allowed. This is a 4f electron.
For nodes, NCERT gives (n − l − 1) radial nodes and l angular nodes, n − 1 in total. A 3p orbital has 1 radial and 1 angular node; a 4d orbital has 1 radial and 2 angular.
In what order do orbitals fill?
NCERT's (n + l) rule: the orbital with the lower n + l fills first; if two have the same n + l, the one with lower n fills first. So 4s (4 + 0 = 4) fills before 3d (3 + 2 = 5), and 3d (n = 3) fills before 4p (also 5, but n = 4).
Two more rules apply as you fill:
Pauli exclusion principle: no two electrons in an atom have the same four quantum numbers, so each orbital holds at most two, with opposite spins. Wolfgang Pauli received the 1945 Nobel Prize in Physics "for the discovery of the Exclusion Principle, also called the Pauli Principle".
Hund's rule: in a set of equal-energy orbitals, electrons occupy them singly, with parallel spins, before pairing.
Example 3. Iron, Z = 26: 1s² 2s² 2p⁶ 3s² 3p⁶ 3d⁶ 4s². By Hund's rule, the six 3d electrons fill five orbitals as four singles and one pair, so iron has 4 unpaired electrons.
Why are chromium and copper exceptions?
By the n + l rule, chromium would be 3d⁴4s² and copper 3d⁹4s². NCERT gives the observed configurations as 3d⁵4s¹ and 3d¹⁰4s¹. Half-filled and completely filled subshells are extra stable, which NCERT links to their symmetry and to exchange energy: electrons with parallel spins in equal-energy orbitals can exchange positions, and each exchange lowers the energy. A half-filled d⁵ set has the most such exchanges.
Which electrons does an ion lose first?
Not the last ones in. The NCERT Class 12 chapter on d- and f-block elements notes that when transition metals form ions, ns electrons are lost before (n − 1)d electrons. So Fe²⁺ is [Ar] 3d⁶, not [Ar] 3d⁴4s², and Fe³⁺ is [Ar] 3d⁵. Filling order and removal order are different things.
Why does this topic feel slippery?
You are not alone if orbitals feel abstract. In interviews with college students in the UK, Taber (2002) found that capable, motivated students struggled to make sense of quantised energy, orbitals and quantum numbers even with experienced teachers, and called it a genuine teaching problem. The practical answer is to tie each rule to a picture, a shape, a box diagram, rather than a string of symbols.
Which mistakes cost marks?
mₗ outside −l to +l, or l equal to n.
Pairing too early in box diagrams, against Hund's rule.
Chromium and copper written by the plain n + l rule.
Removing 3d electrons first when forming transition-metal ions.
Counting total nodes as radial nodes.
A practice routine
Day 1: list all allowed sets of quantum numbers for n = 3, then check against the count of 18.
Day 2: write configurations and box diagrams for Z = 1 to 30, and the number of unpaired electrons for each.
Day 3: ions: Fe²⁺, Fe³⁺, Cu⁺, Cu²⁺, Cr³⁺, Mn²⁺, Zn²⁺.
Day 4: nodes for 2s, 3p, 3d, 4s, 4f.
Day 5: make flashcards that test you for the exceptions and their reasons.
The history helps too; our post on Niels Bohr's atom model shows where quantised shells came from, and periodic trends and their exceptions shows what configurations explain. If an idea still will not settle, the Fermi Concept Library has every concept in chemistry, each with its own lesson and its place in the map.
Today, write the configuration of Mn²⁺ and count its unpaired electrons.
