GUJCET flashcards

32 cards. Read the term and the definition here. The deck at the top of this page is optional.

Escape velocity

Minimum speed at a planet's surface for a body to escape its gravity without further propulsion: v = √(2GM/R) = √(2gR), about 11.2 km/s for Earth, independent of the body's mass.

Projectile maximum range

For a projectile launched over level ground at fixed speed u, range R = u² sin2θ/g is largest at θ = 45°, giving R_max = u²/g; complementary angles give equal ranges.

Kirchhoff's junction rule

At any circuit node the algebraic sum of currents is zero, ΣI = 0; it expresses conservation of charge, because charge does not pile up at a junction in the steady state.

Stopping potential

The reverse voltage V₀ that just stops the fastest emitted photoelectrons; eV₀ = hν − φ, so V₀ rises with frequency and depends on the metal but not on light intensity.

Series LCR resonance

At f = 1/(2π√(LC)) the inductive and capacitive reactances cancel, impedance falls to R, current is maximum, and the power factor cos φ equals 1.

Gauss's law

Total electric flux through any closed surface equals enclosed charge divided by ε₀; applied to an infinite sheet it gives E = σ/2ε₀, and inside a conductor E = 0.

Bohr radius

The n-th hydrogen orbit has radius r_n = 0.529 n² Å, so the ground state is 0.529 Å, with corresponding energy E_n = −13.6/n² eV.

Work-energy theorem

The net work done by all forces acting on a body equals its change in kinetic energy, W_net = ½mv² − ½mu²; the result also holds for variable forces.

Capacitance with dielectric

Filling a capacitor gap with a dielectric of constant κ multiplies capacitance by κ, so C = κε₀A/d; at fixed voltage charge increases, at fixed charge voltage falls.

Critical angle

For light going from a denser medium of refractive index n into a rarer one, total internal reflection starts at angle C where sin C = 1/n.

de Broglie wavelength

A particle with momentum p = mv has associated wavelength λ = h/p = h/mv; greater mass or speed means a shorter wavelength, so large objects show no measurable diffraction.

Molality

Moles of solute per kilogram of solvent, m = n/kg; being mass-based, it stays fixed when temperature changes, unlike molarity, and is used for colligative-property calculations.

Gibbs energy criterion

At constant temperature and pressure a process is spontaneous when ΔG = ΔH − TΔS is negative; ΔG = 0 at equilibrium and ΔG° = −RT ln K.

First-order half-life

For a first-order reaction t½ = 0.693/k, independent of starting concentration; after n half-lives the fraction of reactant remaining is (1/2)^n.

Henderson-Hasselbalch equation

For an acidic buffer pH = pKa + log([salt]/[acid]); for a basic buffer pOH = pKb + log([salt]/[base]). Buffer capacity is best when pH equals pKa.

Markovnikov's rule

In addition of HX to an unsymmetrical alkene, hydrogen attaches to the carbon already bearing more hydrogens, forming the more stable carbocation; peroxide makes only HBr add anti-Markovnikov.

SN2 mechanism

Single-step nucleophilic substitution in which the nucleophile attacks opposite the leaving group, inverting the configuration; rate is proportional to both substrate and nucleophile, and primary halides react fastest.

Packing efficiency of fcc

Face-centred cubic (ccp) has atoms at corners and face centres, Z = 4, coordination number 12, and 74% of the space occupied, the maximum for equal spheres.

Nernst equation at 298 K

E_cell = E°_cell − (0.0591/n) log Q, where n is the number of electrons transferred and Q the reaction quotient; E°_cell = E°_cathode − E°_anode.

sp² hybridisation

Mixing one s and two p orbitals gives three sp² hybrids lying 120° apart in a plane, leaving one unhybridised p orbital that forms a π bond, as in ethene.

Le Chatelier's principle

When an equilibrium system is disturbed by changed concentration, pressure or temperature, it shifts to partially oppose that change; a catalyst speeds both directions without shifting the position of equilibrium.

Lucas test

Shaking an alcohol with concentrated HCl and anhydrous ZnCl₂ gives cloudiness of alkyl chloride: tertiary alcohols react immediately, secondary within minutes, primary only on heating.

Derivative of arcsin x

d/dx(sin⁻¹x) = 1/√(1 − x²) for |x| < 1; correspondingly d/dx(cos⁻¹x) = −1/√(1 − x²) and d/dx(tan⁻¹x) = 1/(1 + x²).

Conditional probability

P(A|B) = P(A ∩ B)/P(B), defined when P(B) > 0; events A and B are independent exactly when P(A ∩ B) = P(A)P(B), so P(A|B) reduces to P(A).

Point-line distance formula

The perpendicular distance from (x₁, y₁) to ax + by + c = 0 is |ax₁ + by₁ + c|/√(a² + b²); the numerator vanishes when the point lies on the line.

Inverse of a matrix

For a square matrix A with det A ≠ 0, A⁻¹ = adj A/|A|; a non-zero determinant means the matrix is invertible and Ax = b has a unique solution.

Dot product

a·b = |a||b| cos θ = a₁b₁ + a₂b₂ + a₃b₃; it equals zero for perpendicular vectors, and the projection of a along b is (a·b)/|b|.

Test cross

Crossing an individual of unknown genotype with the homozygous recessive parent; all dominant offspring indicate homozygosity, while a 1:1 ratio reveals a heterozygote.

Universal blood donor

O-negative red cells, because they lack A, B and Rh D antigens, so recipient antibodies do not attack them; AB-positive people can receive blood of any group.

Calvin cycle location

The dark reactions take place in the chloroplast stroma, where RuBisCO fixes CO₂ onto RuBP and ATP with NADPH from the thylakoid reactions drives reduction and regeneration.

Products of meiosis

One diploid cell undergoes two successive divisions to give four haploid cells, all genetically different because of crossing over in prophase I and independent assortment in metaphase I.

Dihybrid F2 ratio

Crossing two double heterozygotes for independently assorting genes (AaBb × AaBb) yields phenotypes in the ratio 9:3:3:1 and nine different genotypes.