E_n = −13.6 Z²/n² eV
“Fireworks glow in colours because excited electrons drop back and release exact packets of light.”
Energy of an electron in a hydrogen-like atom. Use it when single-electron (H-like) species.
E_n = −13.6 Z²/n² eV
Fundamentals
The core facts every aspirant should own — each a titled nugget with a real-world story, the concept in plain words, and a memory trick. Works even when the internet doesn't.
1,200 fundamentals
“Fireworks glow in colours because excited electrons drop back and release exact packets of light.”
Energy of an electron in a hydrogen-like atom. Use it when single-electron (H-like) species.
E_n = −13.6 Z²/n² eV
“Fireworks glow in colours because excited electrons drop back and release exact packets of light.”
An orbit is a fixed Bohr path (outdated); an orbital is a 3-D region of high probability for finding an electron.
“Fireworks glow in colours because excited electrons drop back and release exact packets of light.”
A shell is a principal energy level (n); a subshell (s, p, d, f) is a division within a shell.
“Fireworks glow in colours because excited electrons drop back and release exact packets of light.”
Aufbau decides the ORDER subshells fill (low to high energy); Hund decides HOW electrons spread within a subshell (singly, same spin).
“Fireworks glow in colours because excited electrons drop back and release exact packets of light.”
Chromium is 3d⁵ 4s¹ and copper 3d¹⁰ 4s¹ — half/fully-filled d subshells are extra stable.
“Water is bent, not straight — and that single fact is why life exists.”
Atoms tend to gain, lose or share electrons to reach eight in their outer shell.
Memory trick: the octet rule is a guide, not a law — watch for electron-deficient and expanded-octet molecules.
“Water is bent, not straight — and that single fact is why life exists.”
A frequent error is forcing an octet on exceptions like BeCl₂, BF₃ or SF₆. In reality, atoms tend to gain, lose or share electrons to reach eight in their outer shell.
Memory trick: the octet rule is a guide, not a law — watch for electron-deficient and expanded-octet molecules.
“Water is bent, not straight — and that single fact is why life exists.”
A frequent error is counting only bonding pairs and ignoring lone pairs. In reality, electron pairs around a central atom arrange to be as far apart as possible, fixing the molecule's shape.
Memory trick: lone pairs take more room and squeeze bond angles smaller.
“Water is bent, not straight — and that single fact is why life exists.”
Atomic orbitals mix to form equivalent hybrid orbitals (sp, sp², sp³) that set the geometry.
Memory trick: sp³ → tetrahedral, sp² → trigonal planar, sp → linear.
“Water is bent, not straight — and that single fact is why life exists.”
A frequent error is predicting geometry without counting lone pairs in the hybridization. In reality, atomic orbitals mix to form equivalent hybrid orbitals (sp, sp², sp³) that set the geometry.
Memory trick: sp³ → tetrahedral, sp² → trigonal planar, sp → linear.
“Water is bent, not straight — and that single fact is why life exists.”
A molecule is polar only if bond dipoles don't cancel, which depends on both electronegativity and shape.
Memory trick: symmetry can cancel dipoles — shape matters as much as bonds.
“Water is bent, not straight — and that single fact is why life exists.”
A frequent error is calling any molecule with polar bonds a polar molecule. In reality, a molecule is polar only if bond dipoles don't cancel, which depends on both electronegativity and shape.
Memory trick: symmetry can cancel dipoles — shape matters as much as bonds.
“Water is bent, not straight — and that single fact is why life exists.”
A frequent error is treating hydrogen bonds as ordinary covalent bonds. In reality, a strong dipole attraction when H is bonded to N, O or F.
Memory trick: hydrogen bonding explains water's unusually high boiling point.
“Water is bent, not straight — and that single fact is why life exists.”
An ionic bond transfers electrons (metal + non-metal, forms ions); a covalent bond shares electrons (between non-metals).
“Water is bent, not straight — and that single fact is why life exists.”
A sigma bond forms by head-on overlap and is strong; a pi bond forms by sideways overlap of p-orbitals and is weaker.
“Water is bent, not straight — and that single fact is why life exists.”
A polar molecule has a net dipole (water); a non-polar one has none because its dipoles cancel (CO₂).
“Water is bent, not straight — and that single fact is why life exists.”
Its C=O bonds are polar, but the linear shape makes the dipoles cancel, so CO₂ is non-polar.
“An instant cold-pack turns freezing because it steals heat — an endothermic reaction in your hand.”
The heat content at constant pressure; ΔH is negative for exothermic and positive for endothermic reactions.
Memory trick: heat released → ΔH negative; heat absorbed → ΔH positive.
“An instant cold-pack turns freezing because it steals heat — an endothermic reaction in your hand.”
A frequent error is getting the sign of ΔH the wrong way round. In reality, the heat content at constant pressure; ΔH is negative for exothermic and positive for endothermic reactions.
Memory trick: heat released → ΔH negative; heat absorbed → ΔH positive.
“An instant cold-pack turns freezing because it steals heat — an endothermic reaction in your hand.”
A measure of disorder or the number of ways energy can be arranged.
Memory trick: it's the total entropy (system + surroundings) that rises in a spontaneous change.
“An instant cold-pack turns freezing because it steals heat — an endothermic reaction in your hand.”
A frequent error is thinking entropy always increases for the system alone. In reality, a measure of disorder or the number of ways energy can be arranged.
Memory trick: it's the total entropy (system + surroundings) that rises in a spontaneous change.
“An instant cold-pack turns freezing because it steals heat — an endothermic reaction in your hand.”
A frequent error is judging spontaneity from ΔH alone. In reality, ΔG = ΔH − TΔS decides spontaneity — negative ΔG means the process is spontaneous.
Memory trick: an endothermic reaction can still be spontaneous if TΔS is large enough.
“An instant cold-pack turns freezing because it steals heat — an endothermic reaction in your hand.”
A frequent error is thinking ΔH depends on the reaction path. In reality, the total enthalpy change is the same no matter the route taken.
Memory trick: enthalpy is a state function — add steps freely.
“An instant cold-pack turns freezing because it steals heat — an endothermic reaction in your hand.”
Gibbs free energy change deciding spontaneity. Use it when constant temperature and pressure.
ΔG = ΔH − TΔS