KCET flashcards

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

Projectile maximum range

For a projectile launched and landing at the same height, range R = u²sin2θ/g is greatest at θ = 45°, giving R_max = u²/g.

Centripetal acceleration

In uniform circular motion the acceleration magnitude is v²/r = ω²r, directed toward the center; it changes direction of velocity but not its magnitude.

Elastic versus inelastic collision

Momentum is conserved in both. Kinetic energy is conserved only in elastic collisions; in perfectly inelastic collisions the bodies stick together and lose maximum kinetic energy.

Photoelectric threshold frequency

Emission occurs only when incident frequency ν exceeds the threshold ν₀ = φ/h, where φ is the work function. Below ν₀, no electrons are emitted no matter how intense the light.

Lens power in diopters

Power P = 1/f when focal length f is in meters. A converging lens has positive power; a diverging lens has negative power. Diopter units are m⁻¹.

Radioactive half-life

After n half-lives the remaining nuclei are N₀(1/2)ⁿ. Activity A = λN, and the decay constant λ = 0.693/T, where T is the half-life.

Ohm's law and resistivity

V = IR for ohmic conductors at constant temperature. Resistivity ρ = RA/L is a material property, while resistance also depends on length and cross-sectional area.

Work-energy theorem

The net work done by all forces equals the change in kinetic energy: W_net = ½mv² − ½mu². This holds even when forces vary, using work as the integral of force.

Mole concept at STP

One mole contains 6.022×10²³ particles and equals mass divided by molar mass. At STP an ideal gas occupies 22.4 L per mole.

Ideal gas law

PV = nRT, with R = 0.0821 L·atm/(mol·K) or 8.314 J/(mol·K). Temperature must be in kelvin; pressure and volume units must match the chosen R.

Le Chatelier's principle

A system at equilibrium shifts to oppose a disturbance: adding reactant shifts forward, raising pressure favors fewer gas moles, and a catalyst only speeds attainment of equilibrium.

Bond order from MO theory

Bond order = (bonding electrons − antibonding electrons)/2. Higher bond order means a shorter, stronger bond; bond order zero predicts the molecule does not exist.

SN1 versus SN2 mechanism

SN1 is two-step via a carbocation, favored by tertiary carbons and polar protic solvents, giving racemization. SN2 is one-step, favored by primary carbons, with inversion of configuration.

Oxidation and reduction agents

The oxidizing agent gains electrons and is itself reduced; the reducing agent loses electrons and is oxidized. Track oxidation numbers to identify which species changes.

pH of strong acid

pH = −log[H⁺]. For a strong monobasic acid of concentration C, pH = −log C. At 25 °C, pH + pOH = 14 for any aqueous solution.

Electron configuration filling order

Aufbau order is 1s 2s 2p 3s 3p 4s 3d 4p, so 4s fills before 3d. Hund's rule places one electron in each degenerate orbital before pairing.

Derivative of x to the n

d/dx(xⁿ) = nxⁿ⁻¹ for any real n. Combined with the chain rule, this handles composite powers such as (3x+1)⁵, whose derivative is 15(3x+1)⁴.

Second derivative test

At a critical point where f'(x) = 0, f''(x) > 0 indicates a local minimum and f''(x) < 0 indicates a local maximum. If f''(x) = 0, the test is inconclusive.

Integration by parts

∫u dv = uv − ∫v du. Choose u by LIATE order: logarithmic, inverse trigonometric, algebraic, trigonometric, exponential, so the remaining integral is simpler.

Perpendicular line slopes

Two non-vertical lines are perpendicular exactly when the product of their slopes is −1, so the perpendicular slope is the negative reciprocal of the original slope.

Ellipse eccentricity

For x²/a² + y²/b² = 1 with a > b, eccentricity e = √(1 − b²/a²). Eccentricity lies between 0 and 1; a circle has e = 0.

Conditional probability formula

P(A|B) = P(A∩B)/P(B) for P(B) > 0. Bayes' theorem uses this to reverse conditioning: P(A|B) = P(B|A)P(A)/P(B).

Sum of squares formula

Σn² from 1 to n equals n(n+1)(2n+1)/6, while Σn equals n(n+1)/2. These closed forms simplify limits and series problems quickly.

Standard limit sin x over x

As x approaches 0, sin x/x approaches 1, and (1+x)^(1/x) approaches e. These standard limits underlie derivatives of trigonometric and exponential functions.

Photosystem II water splitting

In the light reaction, photosystem II splits water, releasing O₂ as a by-product and supplying electrons; the electron flow produces ATP and NADPH for the Calvin cycle.

ATP yield of respiration

Glycolysis yields a net 2 ATP in the cytosol, the Krebs cycle runs in the mitochondrial matrix, and oxidative phosphorylation on the inner membrane yields most of the roughly 36 ATP.

Dihybrid cross ratio

Crossing two heterozygotes for two independently assorting genes gives a 9:3:3:1 F₂ phenotypic ratio; a monohybrid cross gives 3:1.

Semiconservative DNA replication

Each new DNA molecule keeps one parental strand and one newly synthesized strand. Adenine pairs with thymine by two hydrogen bonds; guanine pairs with cytosine by three.

Codon reading direction

Ribosomes read mRNA codons in the 5' to 3' direction and assemble protein from the N-terminus to the C-terminus, using tRNA anticodons matched by base pairing.

Blood flow through the heart

Right atrium to right ventricle to pulmonary artery to lungs, then left atrium to left ventricle to aorta. Arteries carry blood away from the heart regardless of oxygenation.

Nephron segment order

Filtrate passes Bowman's capsule, proximal tubule, loop of Henle, distal tubule, and collecting duct. Most reabsorption of glucose, water, and ions occurs in the proximal tubule.

Sodium-potassium pump

The Na⁺/K⁺ ATPase moves three Na⁺ out and two K⁺ in per ATP, maintaining resting membrane potential. Action potentials depolarize through rapid Na⁺ influx.