Lesson 12 of 12 · 17 min

Chapter review

Watch a class

The whole chapter on YouTube

Whole chapter in ninety minutes, NEET pace
Competition Wallah · Hinglish · Whole chapter · Open on YouTube

Full chapter revision for CBSE boards
Next Toppers - 11th Science · Hinglish · Whole chapter · Open on YouTube

Must-know facts

19 facts

1e/mₑ = 1.758820 × 10¹¹ C kg⁻¹; e = 1.602176 × 10⁻¹⁹ C; mₑ = 9.1094 × 10⁻³¹ kg.
2Masses in u: electron 0.00054, proton 1.00727, neutron 1.00867; the neutron is slightly heavier than the proton.
3Chadwick (1932) found the neutron by hitting beryllium with α-particles.
4In the gold-foil experiment about 1 in 20,000 α-particles bounced back; nucleus about 10⁻¹⁵ m, atom about 10⁻¹⁰ m.
5Neutrons = A − Z for atoms and ions alike; isotopes share Z, isobars share A.
6Hydrogen isotopes: protium 99.985%, deuterium 0.015%, tritium in traces.
7c = νλ with c = 3.0 × 10⁸ m s⁻¹; visible light spans 400-750 nm, or 7.5 × 10¹⁴ to 4.0 × 10¹⁴ Hz.
8E = hν, h = 6.626 × 10⁻³⁴ J s; one mole of photons at 5 × 10¹⁴ Hz carries about 199.5 kJ.
9hν = W₀ + ½mₑv²; kinetic energy depends on frequency, number of electrons on brightness.
10Balmer series (n₁ = 2) is the only visible hydrogen series; Lyman (n₁ = 1) is ultraviolet; Paschen, Brackett, Pfund are infrared.
11Rydberg constant for hydrogen: 109,677 cm⁻¹; in energy form 2.18 × 10⁻¹⁸ J.
12Bohr: rₙ = 52.9 n²/Z pm and Eₙ = −2.18 × 10⁻¹⁸ Z²/n² J; He⁺ n = 1 has E = −8.72 × 10⁻¹⁸ J and r = 26.45 pm.
13The n = 5 to n = 2 hydrogen line has ν ≈ 6.91 × 10¹⁴ Hz (about 434 nm).
14λ = h/mv; Δx·Δp ≥ h/4π.
15Shell n has n subshells, n² orbitals and at most 2n² electrons; a subshell has 2l + 1 orbitals.
16Radial nodes = n − l − 1, angular nodes = l, total nodes = n − 1.
17(n + l) rule: lower sum first; tie goes to lower n (so 4s before 3d, 4f before 5d).
18Cr 3d⁵ 4s¹ and Cu 3d¹⁰ 4s¹ are the exceptions to learn.
19Hund's rule: pairing begins with the 4th p, 6th d and 8th f electron.

Common traps

Where marks are lost

Brighter light gives photoelectrons more kinetic energy.

Brightness only adds photons, so more electrons come out. Each electron's kinetic energy is set by frequency: KE = hν − W₀.

Light below the threshold frequency will eject electrons if it shines long enough or brightly enough.

Below ν₀ no single photon has enough energy, and photons do not pool their energy, so nothing is ejected at any brightness or time.

Neutrons in an ion = A − (number of electrons).

Neutrons are always A − Z. Find Z from the protons; the charge only tells you how electrons differ from protons.

The Balmer series ends on n = 1.

Balmer ends on n = 2 and is visible; Lyman ends on n = 1 and is ultraviolet. Remember L-B-P-B-P for n₁ = 1 to 5.

A more negative orbit energy means a less stable electron.

Zero is the free electron at rest; the more negative the energy, the more tightly bound and stable the electron, so n = 1 is the most stable.

Bohr's formula works for He or Li atoms.

It works only for one-electron species: H, He⁺, Li²⁺, Be³⁺. Neutral He has two electrons and Bohr's model fails for it.

3p has two radial nodes because n = 3.

Radial nodes = n − l − 1 = 3 − 1 − 1 = 1; the other node of 3p is angular (l = 1). Total nodes = n − 1 = 2.

3d fills before 4s because 3 is smaller than 4.

Use n + l: 4s has 4 + 0 = 4 and 3d has 3 + 2 = 5, so 4s fills first.

Cr is [Ar] 3d⁴ 4s² and Cu is [Ar] 3d⁹ 4s².

Half-filled and full d subshells are extra stable, so Cr is [Ar] 3d⁵ 4s¹ and Cu is [Ar] 3d¹⁰ 4s¹.

Orbit and orbital mean the same thing.

An orbit is Bohr's definite circular path, which the uncertainty principle rules out; an orbital is a wave function whose square gives the probability of finding the electron.

Formulas

13 to know

Mass number

A = Z + (number of neutrons)

Z = protons = electrons in a neutral atom.

Wave relation

c = νλ; ν̄ = 1/λ

c = 3.0 × 10⁸ m s⁻¹; ν̄ usually in cm⁻¹.

Planck's quantum

E = hν = hc/λ

h = 6.626 × 10⁻³⁴ J s; multiply by Nₐ = 6.022 × 10²³ mol⁻¹ for a mole of photons.

Photoelectric equation

hν = hν₀ + ½mₑv²

hν₀ = W₀, the work function; no emission if ν < ν₀.

Rydberg formula (hydrogen)

ν̄ = 109,677 (1/n₁² − 1/n₂²) cm⁻¹

n₂ > n₁; n₁ = 1, 2, 3, 4, 5 gives Lyman, Balmer, Paschen, Brackett, Pfund.

Bohr angular momentum

mₑvr = nh/2π

n = 1, 2, 3 …

Bohr radius

rₙ = 52.9 n²/Z pm

Z = 1 for hydrogen; one-electron species only.

Bohr energy

Eₙ = −2.18 × 10⁻¹⁸ (Z²/n²) J

E = 0 at n = ∞; ionisation energy of H from n = 1 is 2.18 × 10⁻¹⁸ J per atom.

Transition energy and frequency

ΔE = 2.18 × 10⁻¹⁸ (1/nᵢ² − 1/n_f²) J; ν = 3.29 × 10¹⁵ (1/nᵢ² − 1/n_f²) Hz

Negative ΔE is emission, positive is absorption.

de Broglie wavelength

λ = h/mv = h/p

Detectable only for very small masses.

Uncertainty principle

Δx · Δp ≥ h/4π; Δx · Δv ≥ h/4πm

Negligible for everyday masses.

Node count

radial = n − l − 1; angular = l; total = n − 1

l = 0, 1, 2, 3 for s, p, d, f.

Capacity

orbitals per subshell = 2l + 1; orbitals per shell = n²; electrons per shell = 2n²

Two electrons of opposite spin per orbital.

Key terms

15 terms

Cathode rays: The stream of electrons that flows from cathode to anode in a low-pressure discharge tube.
Canal rays: Positive gaseous ions formed in a discharge tube, whose mass depends on the gas used.
Isotopes: Atoms of one element with the same atomic number but different mass numbers.
Isobars: Atoms of different elements that share the same mass number.
Quantum: The smallest packet of energy that can be emitted or absorbed as radiation, equal to hν.
Work function: The least energy a photon must bring to free an electron from a given metal surface.
Threshold frequency: The lowest light frequency that can eject electrons from a given metal.
Line spectrum: A spectrum of separate bright (or dark) lines at wavelengths characteristic of an element.
Stationary state: In Bohr's model, an allowed orbit in which the electron keeps a fixed energy.
Atomic orbital: A one-electron wave function ψ in an atom, labelled by n, l and mₗ.
Probability density: |ψ|², the probability per unit volume of finding the electron at a point.
Node: A surface on which the probability density of an orbital is zero.
Degenerate orbitals: Orbitals that have exactly the same energy.
Effective nuclear charge: The net positive pull felt by an electron after shielding by the other electrons.
Exchange energy: The stabilisation gained when electrons of the same spin in degenerate orbitals can swap places.

Test yourself: 10 questionsExam-style questions on Structure of Atom, with full solutions.Start