JEE Advanced key terms

A measure of how strongly an object resists a change in its rotational motion about a given axis; it depends on the object's mass and on how that mass is distributed relative to the axis.

The rotational analogue of linear momentum, equal to the cross product of position and momentum for a particle; for a rigid body spinning about a fixed axis it equals moment of inertia times angular velocity.

The ratio of relative speed of separation to relative speed of approach for two colliding bodies along the line of impact; it equals one for elastic and zero for perfectly inelastic collisions.

Oscillation in which the restoring force is directly proportional to displacement from equilibrium and directed opposite to it, so displacement varies sinusoidally with time at a fixed angular frequency.

The change in observed frequency of a wave when the source, the observer, or the medium moves relative to the others; frequency rises on approach and falls on receding.

Complete reflection of light back into a denser medium when it strikes the boundary with a rarer medium beyond the critical angle, where the refracted ray would otherwise graze along the surface.

Superposition of two or more coherent waves giving alternate regions of reinforced and cancelled amplitude; in Young's experiment, path difference of a whole number of wavelengths gives bright fringes.

The charge stored on a conductor per unit potential difference applied to it; for a parallel-plate capacitor it equals permittivity times plate area divided by plate separation.

An electromotive force induced in a conductor moving through a magnetic field, because its free charges experience a magnetic force; for a rod of length L moving with speed v perpendicular to field B it equals BLv.

The average velocity along a conductor that free electrons acquire under an applied electric field, superposed on their random thermal motion; it is small and proportional to the field.

The minimum energy needed to remove an electron from the surface of a metal; in the photoelectric effect, light of frequency below the threshold value cannot eject electrons whatever its intensity.

The wavelength associated with a moving particle, equal to Planck's constant divided by the particle's momentum; it explains electron diffraction and quantisation of angular momentum in Bohr's model.

The mixing of atomic orbitals of similar energy on the same atom to form equivalent new orbitals that point in definite directions, explaining observed molecular geometries and bond angles such as the tetrahedral angle in methane.

Alternative Lewis structures of one molecule that differ only in the placement of electrons, not atoms; the real molecule is a weighted average, more stable than any single contributing structure.

A species that accepts a pair of electrons to form a new bond, typically electron-deficient; it is attacked by electron-rich centres and often carries a positive charge or a partial positive charge.

A species that donates an electron pair to form a new bond, typically electron-rich; it attacks electron-poor centres and its strength depends on charge, solvent and polarisability.

The property of a molecule that is not superimposable on its mirror image, usually arising from a carbon bearing four different groups; the two mirror forms rotate plane-polarised light in opposite directions.

A planar, cyclic, completely conjugated ring is aromatic if it contains 4n+2 pi electrons, where n is a non-negative integer; rings with 4n pi electrons are antiaromatic.

When a system at equilibrium is disturbed by a change in concentration, pressure or temperature, the equilibrium shifts in the direction that partly opposes the change.

The ratio, at equilibrium, of the product of product concentrations each raised to its stoichiometric coefficient to the product of reactant concentrations similarly raised; for a given reaction it depends only on temperature.

The potential of a half-cell measured against the standard hydrogen electrode under standard conditions of unit activity and one bar, conventionally quoted as a reduction potential.

Properties of a solution that depend on the number of dissolved particles rather than their identity, namely relative lowering of vapour pressure, boiling-point elevation, freezing-point depression and osmotic pressure.

The separation in energy of a metal's d orbitals when ligands approach in a complex, caused by different electrostatic repulsion; the size of the gap decides colour and magnetic behaviour.

The slowest elementary step of a multistep reaction mechanism; it controls the overall rate and its species appear in the experimentally observed rate law.

The value a function approaches as its argument approaches a given point, whether or not the function is defined there; limits underlie continuity, derivatives and integrals.

A function is continuous at a point when its limit there exists and equals the function's value at that point; on an interval this means the graph can be drawn without a break.

A function is differentiable at a point when the derivative there exists as a finite two-sided limit; differentiability implies continuity, but continuity does not imply differentiability, as at a sharp corner.

If a function is continuous on a closed interval, differentiable inside it, and takes equal values at both ends, then its derivative vanishes at some interior point.

For a function continuous on a closed interval and differentiable inside, there exists an interior point where the instantaneous rate of change equals the average rate over the interval.

A function, usually an exponential, by which a first-order linear differential equation is multiplied so that the left side becomes the derivative of a single product.

A scalar for which a nonzero vector is mapped to a scalar multiple of itself by a given square matrix; found by solving the characteristic equation.

The number of linearly independent rows, equivalently independent columns, of a matrix; it equals the order of the largest non-vanishing minor.

The dot product of one vector with the cross product of the other two; its absolute value gives the volume of the parallelepiped they span, and it vanishes for coplanar vectors.

A number describing how much a conic deviates from a circle; it is the ratio of the distance to the focus to the distance to the directrix, below one for ellipses and above one for hyperbolas.

A rule giving the conditional probability of a hypothesis after evidence, as the prior probability times the likelihood, divided by the total probability of the evidence.

The probability distribution of the number of successes in a fixed number of independent trials, each with the same two possible outcomes and the same success probability.