NDA Chemistry · Formula sheet

Atomic Structure and Periodic Classification formulas

7 formulas, 9 reference tables and 19 common traps for NDA Chemistry Atomic Structure and Periodic Classification, grouped by subtopic.

Full notes with worked examples

Atomic Models — Dalton, Thomson, Rutherford, Bohr

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Who discovered each subatomic particle and model

Discovery	Scientist	Experiment / note
Electron	J. J. Thomson	Cathode rays; proposed the plum-pudding model
Proton	E. Goldstein	Canal rays (anode rays)
Neutron	James Chadwick	1932; neutral particle in the nucleus NDA 2025 + 2020 — the neutron was discovered by James Chadwick.
Nucleus	Ernest Rutherford	Alpha-particle (gold-foil) scattering experiment NDA 2017 — Rutherford's alpha-scattering experiment discovered the nucleus.

The four atomic models and what each could not explain

Model	Key claim	Could NOT explain
Dalton	Indivisible solid sphere; identical atoms	Subatomic particles (electrons, nucleus)
Thomson (plum pudding)	Positive sphere with electrons embedded	The dense nucleus / scattering of alpha particles
Rutherford (nuclear)	Tiny dense POSITIVE nucleus; mostly empty space	Why electrons don't spiral in; fixed energy orbits Rutherford's nucleus is POSITIVELY charged, not neutral. Fixed energy orbits are a BOHR idea, not Rutherford's.
Bohr	Electrons in fixed circular orbits of definite energy	Spectra of multi-electron atoms (refined later)

Fixed energy orbits = Bohr. Nucleus = Rutherford. Plum pudding = Thomson. Indivisible sphere = Dalton.

Dalton's pictorial element symbols

Element	Dalton's symbol
Phosphorus	Circle with a cross (+) inside (circled cross) NDA 2023 — Dalton's phosphorus is the circle with the + sign inside.
Oxygen	A plain open circle
Hydrogen	A circle with a central dot
Sulphur	A circle with a letter mark inside

Common traps

Chadwick = neutron, not Rutherford

Rutherford discovered the nucleus; the neutron was discovered later by James Chadwick (1932). Don't credit Rutherford with the neutron.

Rutherford's nucleus is positive, not neutral

A statement that 'there is a neutral centre in an atom called the nucleus' is NOT part of Rutherford's model — his nucleus carries the atom's positive charge.

Fixed-energy orbits belong to Bohr

When a question asks what Rutherford's model could NOT explain (or which finding is not his), the answer is almost always electrons in fixed-energy orbits — that came from Bohr.

Atomic Number, Mass Number and Subatomic Particles

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Atomic number, mass number and counting nucleons

Mass number and neutron count

A = Z + N \qquad N = A - Z \qquad e^-_{\text{(ion)}} = Z - (\text{charge})

$A$ mass number (nucleons)
$Z$ atomic number (protons)
$N$ number of neutrons

Formula mass and reading valency from the atom

Formula mass

\text{Formula mass} = \sum (\text{atomic mass} \times \text{number of atoms})

Average atomic mass from isotope proportions

Weighted average atomic mass

\bar{M} = \frac{m_1 f_1 + m_2 f_2}{f_1 + f_2}

$m_1, m_2$ isotope masses
$f_1, f_2$ their proportions (parts of the ratio)

The three subatomic particles — charge, mass and location

Particle	Charge	Relative mass	Location
Proton	+1	≈ 1 u	Nucleus
Neutron	0 (neutral)	≈ 1 u	Nucleus
Electron	−1	≈ 1/2000 of a proton	Shells outside the nucleus NDA 2025 — the mass of an electron is about 1/2000 (precisely 1/1836) that of a proton.

Protons + neutrons = nucleons, carrying nearly all the mass. Electrons are almost massless.

Common traps

A neutron is not a proton + electron

'A neutron is formed by combination of an electron and a proton, therefore it is neutral' is false. The neutron is a distinct fundamental particle.

Atomic mass = protons + neutrons, not + electrons

The atomic mass is the sum of protons and neutrons only. Electrons are about 1/2000 the mass of a nucleon, so they contribute nothing — do not add electrons.

Charge changes electrons, not nucleons

A 2− or 3+ charge changes the electron count, never the proton or neutron count. The mass number (nucleons) of an ion equals that of its neutral atom.

Aluminium's valency is 3, not 2

From the configuration 2,8,3, aluminium loses 3 electrons to reach an octet — valency 3. A statement claiming 'the valency of Al is 2' is the false one.

Weight by proportion, don't just average the masses

For a 3 : 1 mix of 16 u and 18 u the answer is 16.5 u, not the plain mean 17 u. Always multiply each mass by its fraction (3/4 and 1/4) before adding.

Isotopes and Isoelectronic Species

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Average atomic mass and finding isotope abundance

Weighted average and back-solving abundance

\bar{M} = \frac{m_1 x + m_2 (100 - x)}{100}

$\bar{M}$ average atomic mass
$m_1, m_2$ isotope masses
$x$ percentage abundance of isotope 1

Isotopes, isobars and isoelectronic species — the definitions

Term	What is the same	What differs	Example
Isotopes	Protons (Z) — same element	Neutrons / mass number	³⁵Cl and ³⁷Cl
Isobars	Mass number (A)	Element / proton count	⁴⁰Ar and ⁴⁰Ca
Isoelectronic	Number of electrons	Element and charge	Na⁺, F⁻, O²⁻, Ne (all 10 e⁻) To test isoelectronic species, just count electrons: protons minus the charge.

Useful radioactive isotopes

Isotope	Main use
Cobalt-60	Cancer treatment (radiotherapy) NDA 2020 — the isotope used to treat cancer is cobalt-60. (Cobalt, not iodine.)
Iodine-131	Treating thyroid disorders
Carbon-14	Radiocarbon dating of fossils
Uranium-235	Nuclear fuel (fission)

Common traps

N⁻ is NOT isoelectronic with F⁻

F⁻ has 10 electrons (9 + 1). N⁻ has only 7 + 1 = 8 electrons, so it is the odd one out. Always recount: protons ± charge.

Isotopes vs isobars vs isoelectronic

Same protons → isotopes. Same mass number → isobars. Same electrons → isoelectronic. Mixing these up is the most common slip here.

Read the order of the answer

For boron the abundances are 19% ¹⁰B and 81% ¹¹B — the heavier isotope is the more common one. Options often swap the order (81% and 19%); match each percentage to the right isotope.

Cobalt-60 for cancer, iodine-131 for thyroid

The cancer-treatment isotope is cobalt-60, not iodine. Iodine-131 is the thyroid one. The bank lists both as options.

Electron Configuration and Valence Shells

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Maximum electrons in a shell (the 2n² rule)

Maximum electrons per shell

\text{Maximum electrons} = 2n^2

$n$ shell number (K=1, L=2, M=3, N=4)

Valence-shell electrons and bonding from the configuration

Electrons gained/lost to reach an octet

\text{Valency} = 8 - (\text{valence electrons}) \;\text{ or }\; (\text{valence electrons})

Common traps

2n² is a CAP, not the actual filling

The 2n² rule gives the maximum a shell can hold. In real atoms the outermost shell never holds more than 8 before the next shell starts filling — but the capacity question asks for the cap (M = 18, N = 32).

Valence electrons live in the OUTERMOST shell only

For Z = 35 the configuration is 2, 8, 18, 7 — the M shell holds 18, but the valence shell is the N shell with 7. Count only the outermost shell, not the largest.

Periodic Trends, Valency and Atomicity

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Valency, groups and the most fundamental property

Standard valencies by group

\text{Ne}=0 \quad \text{Mg}=2 \quad \text{N}=3 \quad \text{Si}=4

Atomicity — atoms per molecule of a free element

Element	Molecule	Atomicity
Neon	Ne	1 (monatomic)
Nitrogen	N₂	2 (diatomic)
Chlorine	Cl₂	2 (diatomic)
Iodine	I₂	2 (diatomic)
Phosphorus	P₄	4 (tetra-atomic, polyatomic) NDA 2024 — phosphorus is the polyatomic element (P₄), unlike diatomic Cl₂ or metallic Al.
Sulphur	S₈	8 (octa-atomic, polyatomic)

Noble gases = 1; common gases = 2; phosphorus = 4; sulphur = 8.

Reactivity and oxidising-power trends

Trend	Direction down the group	Extreme the bank asks for
Halogen oxidising power	Decreases (F strongest, I weakest)	Increasing order: I < Br < Cl < F NDA 2023 — increasing oxidising order of halogens is I, Br, Cl, F.
Alkali-metal reactivity with water	Increases (Li least, Cs most)	Lithium is least reactive with water NDA 2017 — among alkali metals, lithium is the least reactive with water.

Noble gases — inertness and uses

Noble gas	Signature use
Argon	Fills bulbs so the tungsten filament lasts longer
Neon	Advertising / neon signs
Krypton	Airport landing lights and lighthouses
Xenon	Photographer's flash gun
Radon	An inert (noble) gas; also radioactive NDA 2017 — radon is an inert gas (Group 18).

Common traps

Same group = same valency

Mg, Ca and Ba are all Group 2, so they share valency 2 and form MgCl₂, CaCl₂, BaCl₂. A set like (Na, Mg, Al) spans three groups and three valencies — not the answer.

Phosphorus is P₄, sulphur is S₈

The two polyatomic elements the bank loves are phosphorus (P₄, atomicity 4) and sulphur (S₈, atomicity 8). Don't call them diatomic.

Iodine is diatomic, not monatomic

Only the noble gases (He, Ne, Ar…) are monatomic. Iodine is I₂ (diatomic), so in a 'which is NOT monatomic' question, iodine is the answer.

Oxidising power falls down the group, reactivity rises

For halogens (non-metals), oxidising power decreases down the group (F is best). For alkali metals, reactivity with water increases down the group (Li is least, Cs most). Don't mix the two directions.

Argon protects the filament; neon makes the glow

Argon fills the bulb (inert, prevents the tungsten filament burning out); neon is the one used in glowing advertising signs. The bank swaps these in match-the-list questions.

Atomic Structure and Periodic Classification formulas

Atomic Models — Dalton, Thomson, Rutherford, Bohr

Who discovered each subatomic particle and model

The four atomic models and what each could not explain

Dalton's pictorial element symbols

Common traps

Atomic Number, Mass Number and Subatomic Particles

Atomic number, mass number and counting nucleons

Formula mass and reading valency from the atom

Average atomic mass from isotope proportions

The three subatomic particles — charge, mass and location

Common traps

Isotopes and Isoelectronic Species

Average atomic mass and finding isotope abundance

Isotopes, isobars and isoelectronic species — the definitions

Useful radioactive isotopes

Common traps

Electron Configuration and Valence Shells

Maximum electrons in a shell (the 2n² rule)

Valence-shell electrons and bonding from the configuration

Common traps

Periodic Trends, Valency and Atomicity

Valency, groups and the most fundamental property

Atomicity — atoms per molecule of a free element

Reactivity and oxidising-power trends

Noble gases — inertness and uses

Common traps

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