Structure of the atom for NEET

Structure of the atom is where chemistry starts to explain itself. Periodic trends, bonding, magnetic behaviour, colours of transition metal ions: all of them come back to where the electrons are and how much energy they have. That makes this chapter worth learning properly rather than just memorising.

NEET questions here fall into a few types: which set of quantum numbers is allowed, how many nodes an orbital has, the configuration of an atom or ion (and how many unpaired electrons it has), and short calculations with Bohr's model, the hydrogen spectrum, de Broglie's relation or the uncertainty principle.

Subatomic particles and atomic models

• Atomic number Z = number of protons. Mass number A = protons + neutrons.
• Isotopes: same Z, different A (¹²C, ¹⁴C). Isobars: same A, different Z (¹⁴C, ¹⁴N). Isotones: same number of neutrons.

Thomson's model pictured a sphere of positive charge with electrons embedded in it. Rutherford's alpha-scattering experiment showed that most of the atom is empty space, with its positive charge and nearly all its mass in a tiny nucleus. But Rutherford's model could not explain why an orbiting electron does not radiate energy and spiral into the nucleus, or why atoms give line spectra.

Light, quanta and Bohr's model

Electromagnetic radiation obeys c = νλ, and its wave number is ν̄ = 1/λ. Planck proposed that energy is emitted or absorbed in packets (quanta): E = hν, with h = 6.626 × 10⁻³⁴ J s.

Bohr's model of the hydrogen atom:

• The electron moves in fixed circular orbits (stationary states) without radiating.
• Its angular momentum is quantised: mvr = nh/2π.
• Energy is absorbed or emitted only when the electron jumps between orbits: ΔE = hν.

For hydrogen-like species (one electron, nuclear charge Z):

Lyman lines end on n = 1 (ultraviolet), Balmer on n = 2 (visible), Paschen on n = 3, Brackett on n = 4 and Pfund on n = 5 (all infrared).

Limits of Bohr's model: it works only for one-electron species. It cannot explain the spectra of multi-electron atoms, the splitting of lines in electric and magnetic fields, or the shapes of molecules. And it gives the electron an exact path, which quantum mechanics forbids.

Dual behaviour and uncertainty

• de Broglie: every moving particle has a wavelength λ = h/mv = h/p. It matters only for very small masses such as electrons.
• Heisenberg's uncertainty principle: the position and momentum of an electron cannot both be known exactly. Δx × Δp ≥ h/4π.

Together, these end the idea of fixed orbits. Instead, we speak of the probability of finding an electron in a region of space: an orbital.

Quantum numbers and orbitals

Counting rules: a shell has n² orbitals and holds up to 2n² electrons. A subshell has (2l + 1) orbitals and holds 2(2l + 1) electrons.

Nodes: a node is a region where the probability of finding the electron is zero.

• Radial nodes = n − l − 1
• Angular nodes = l
• Total nodes = n − 1

Shapes: s orbitals are spherical; p orbitals are dumbbell-shaped along x, y and z; four of the five d orbitals are cloverleaf-shaped, and d_z² has two lobes with a ring around the middle.

Energy of orbitals: in hydrogen, energy depends only on n, so 2s and 2p have the same energy. In multi-electron atoms, energy depends on n and l: the lower the (n + l), the lower the energy; if (n + l) is equal, the lower n comes first. So 4s (n + l = 4) fills before 3d (n + l = 5).

Filling electrons: three rules and two exceptions

• Aufbau principle: fill orbitals in order of increasing energy: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, …
• Pauli exclusion principle: no two electrons in an atom have the same four quantum numbers. So an orbital holds at most two electrons, with opposite spins.
• Hund's rule: in degenerate orbitals (such as the three 2p), electrons pair up only after each orbital has one electron.

Exceptions: chromium is [Ar] 3d⁵ 4s¹, not 3d⁴ 4s², and copper is [Ar] 3d¹⁰ 4s¹, not 3d⁹ 4s². Half-filled and completely filled subshells are extra stable because of their symmetry and larger exchange energy.

For the physics side of Bohr's model and matter waves, see dual nature, atoms and nuclei.

Worked NEET-style questions

Example 1: a Balmer line

Find the wavelength of the line emitted when a hydrogen electron falls from n = 4 to n = 2.

• ν̄ = 109,677 × (1/2² − 1/4²) = 109,677 × (1/4 − 1/16) = 109,677 × 3/16 ≈ 20,564 cm⁻¹.
• λ = 1/20,564 cm ≈ 4.86 × 10⁻⁵ cm = 486 nm, a blue-green line in the visible Balmer series.

Example 2: nodes

How many radial and angular nodes does a 3p orbital have?

• Radial = n − l − 1 = 3 − 1 − 1 = 1.
• Angular = l = 1.
• Total = 2, which matches n − 1.

Example 3: unpaired electrons in an ion

How many unpaired electrons does Mn²⁺ have? (Z = 25)

• Mn: [Ar] 3d⁵ 4s². Mn²⁺ loses the two 4s electrons: [Ar] 3d⁵.
• By Hund's rule, the five d electrons occupy the five d orbitals singly: 5 unpaired electrons.

Example 4: de Broglie wavelength of a ball

Find the de Broglie wavelength of a 0.1 kg ball moving at 10 m s⁻¹.

• λ = h/mv = 6.626 × 10⁻³⁴/(0.1 × 10) = 6.6 × 10⁻³⁴ m.
• This is far too small to detect, which is why wave behaviour is noticed only for tiny particles.

Practice MCQs

1. The maximum number of electrons in the n = 3 shell is: (a) 8 (b) 9 (c) 18 (d) 32
2. Which set of quantum numbers is not allowed? (a) n = 2, l = 1, mₗ = 0 (b) n = 3, l = 2, mₗ = −2 (c) n = 2, l = 2, mₗ = 1 (d) n = 4, l = 0, mₗ = 0
3. The number of radial nodes in a 3s orbital is: (a) 0 (b) 1 (c) 2 (d) 3
4. The ground-state configuration of copper (Z = 29) is: (a) [Ar] 3d⁹ 4s² (b) [Ar] 3d¹⁰ 4s¹ (c) [Ar] 3d¹⁰ 4s² (d) [Ar] 3d⁸ 4s²
5. The number of unpaired electrons in nitrogen (1s² 2s² 2p³) is: (a) 1 (b) 2 (c) 3 (d) 5
6. The orbital with n = 4 and l = 3 is: (a) 4s (b) 4p (c) 4d (d) 4f
7. The radius of the second Bohr orbit of He⁺ is: (a) 52.9 pm (b) 105.8 pm (c) 211.6 pm (d) 26.5 pm
8. Which fills first according to the (n + l) rule? (a) 3d (b) 4s (c) 4p (d) they fill together

Answers

1. (c) 2n² = 2 × 9 = 18.
2. (c) For n = 2, l can only be 0 or 1.
3. (c) n − l − 1 = 3 − 0 − 1 = 2.
4. (b) A completely filled 3d subshell is extra stable.
5. (c) Hund's rule puts one electron in each 2p orbital.
6. (d) l = 3 is an f subshell.
7. (b) r = 52.9 × n²/Z = 52.9 × 4/2 = 105.8 pm.
8. (b) 4s has n + l = 4; 3d has 5; 4p has 5.

What to do next

• Write the Aufbau order from 1s to 6p from memory, then check it.
• Write configurations and unpaired electrons for Sc to Zn and their common ions (Fe²⁺, Fe³⁺, Cu⁺, Cu²⁺, Mn²⁺, Cr³⁺).
• Make a nodes table for 1s to 4f.
• Carry this straight into periodic trends, where configurations explain every exception.