Question 1

What are the 4 fundamental kinematic motion equations for constant acceleration?

Accepted Answer

The 4 kinematic equations describe 1D and 2D motion with uniform acceleration (a): 1) v = v₀ + at (velocity as a function of time); 2) Δx = v₀t + ½at² (displacement as a function of time); 3) v² = v₀² + 2aΔx (time-independent velocity-displacement relationship); 4) Δx = ((v₀ + v) / 2) × t (displacement from average velocity). In 2D projectile motion, horizontal motion has a_x = 0, while vertical motion is governed by a_y = -g (-9.80665 m/s² on Earth).

Question 2

How does the Ideal Gas Law (PV = nRT) operate and what are its physical assumptions?

Accepted Answer

The Ideal Gas Law relates the four state variables of a hypothetical ideal gas: Pressure (P in Pa or atm), Volume (V in m³ or L), Amount of substance (n in moles), and Absolute Temperature (T in Kelvin), using the Universal Gas Constant R = 8.314462 J/(mol·K) = 0.082057 L·atm/(mol·K). It assumes point-mass particles with zero volume and perfectly elastic collisions with zero intermolecular attractive forces (accurate for noble gases and atmospheric air at moderate temperatures and pressures).

Question 3

How is molecular Molar Mass calculated from a chemical formula?

Accepted Answer

Molar mass (expressed in grams per mole, g/mol) is the weighted sum of the standard atomic weights of all constituent atoms in one mole of a chemical substance: M = Σ (Atomic Mass_i × Subscript_i). For example, sulfuric acid (H₂SO₄) contains 2 Hydrogens (2 × 1.008 g/mol) + 1 Sulfur (1 × 32.06 g/mol) + 4 Oxygens (4 × 15.999 g/mol) = 98.076 g/mol.

Question 4

How is Circular Orbital Velocity calculated around Earth or other celestial bodies?

Accepted Answer

Circular orbital velocity is determined by equating gravitational centripetal force to gravitational attraction: (m × v²) / r = (G × M × m) / r², which simplifies to v = √(GM / r), where G is the Newtonian gravitational constant (6.67430 × 10⁻¹¹ m³/kg·s²), M is the mass of the central celestial body (e.g. 5.972 × 10²⁴ kg for Earth), and r is the orbital radius from the center of mass (r = Body Radius + Orbital Altitude). For Low Earth Orbit (~400 km altitude for the ISS), v ≈ 7.67 km/s (27,600 km/h).

Question 5

What is the mathematical relationship between Photon Energy, Wavelength, and Frequency?

Accepted Answer

Electromagnetic radiation exhibits wave-particle duality governed by Planck’s relation: E = h × ν = (h × c) / λ, where E is photon energy (in Joules or electron-volts eV), h is Planck’s constant (6.62607 × 10⁻³⁴ J·s), c is the speed of light (2.99792 × 10⁸ m/s), ν is frequency in Hertz (Hz), and λ is wavelength in meters. Because energy is inversely proportional to wavelength, shorter wavelengths (like gamma rays and X-rays) carry exponentially higher quantum energy than radio or microwave photons.

Question 6

What is the formula for calculating Escape Velocity from a planet?

Accepted Answer

Escape velocity (v_e) is the theoretical minimum initial speed required for an unpropelled mass to completely overcome a planet’s gravitational potential well and reach infinite distance with zero residual kinetic energy: v_e = √(2GM / r) = √(2 × g × r). For Earth (mass 5.972 × 10²⁴ kg, mean radius 6,371 km), escape velocity is approximately 11.186 km/s (~25,000 mph). Escape velocity is exactly √2 (≈ 1.414) times the circular orbital speed at that same radius.

Question 7

How do you calculate solution Molarity (M) and prepare a laboratory dilution?

Accepted Answer

Molarity (M) equals moles of solute divided by liters of total solution: M = (Mass of solute in grams / Molar Mass in g/mol) / Solution Volume in Liters. For dilutions, the conservation of solute mass dictates the dilution equation: C₁ × V₁ = C₂ × V₂, where C₁ is initial stock concentration, V₁ is stock volume aliquot, C₂ is target working concentration, and V₂ is final diluted volume.

Question 8

What is the difference between pH and pOH in acid-base chemistry?

Accepted Answer

pH measures the negative base-10 logarithm of hydrogen/hydronium ion activity: pH = -log₁₀[H⁺], while pOH measures hydroxide concentration: pOH = -log₁₀[OH⁻]. In aqueous solutions at standard temperature (25 °C), the autoionization constant of water (K_w = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴) requires that pH + pOH = 14.00. Solutions with pH < 7 are acidic, pH = 7 is neutral pure water, and pH > 7 is basic/alkaline.

Question 9

How is Radioactive Half-Life decay calculated over time?

Accepted Answer

Radioactive decay is a first-order exponential decay process: N(t) = N₀ × (½)^(t / t½) = N₀ × e^(-λt), where N₀ is initial radioactive substance mass or activity, t is elapsed time, t½ is the isotope half-life, and λ = ln(2) / t½ ≈ 0.69315 / t½ is the decay constant. After 1 half-life, 50% remains; after 2 half-lives, 25% remains; after 5 half-lives, only 3.125% remains.

Question 10

What is Snell’s Law of Refraction and how does Total Internal Reflection occur?

Accepted Answer

Snell’s Law calculates the angular bending of light rays passing between media with different refractive indices: n₁ × sin(θ₁) = n₂ × sin(θ₂), where n is refractive index (c / v_medium) and θ is angle measured from the surface normal. When light travels from a higher-index medium to a lower-index medium (n₁ > n₂), there exists a critical angle θ_crit = arcsin(n₂ / n₁). For incident angles θ₁ > θ_crit, no light refracts across the boundary, causing 100% Total Internal Reflection (the foundation of fiber optic cables).

Question 11

What is de Broglie Wavelength and how does it prove matter-wave duality?

Accepted Answer

Louis de Broglie postulated that every moving particle or object exhibits wave characteristics with a matter wavelength given by λ = h / p = h / (m × v), where h is Planck’s constant, p is momentum, m is particle mass, and v is velocity. For subatomic particles like electrons, this wavelength is on the order of picometers to nanometers, enabling electron microscopy with resolving powers 10,000× greater than optical light.

Question 12

What is the Hardy-Weinberg equilibrium principle in genetics?

Accepted Answer

The Hardy-Weinberg law states that allele and genotype frequencies in a sexually reproducing diploid population remain constant across generations in the absence of evolutionary forces (mutation, selection, genetic drift, gene flow, non-random mating). For a two-allele locus: p + q = 1 (allele frequencies) and p² + 2pq + q² = 1 (genotype frequencies), where p² is homozygous dominant (AA), 2pq is heterozygous (Aa), and q² is homozygous recessive (aa).

Question 13

What is Bernoulli’s Principle and how does it relate fluid velocity to pressure?

Accepted Answer

Bernoulli’s equation is a statement of conservation of mechanical energy for inviscid, incompressible fluid flow: P₁ + ½ρv₁² + ρgh₁ = P₂ + ½ρv₂² + ρgh₂, where P is static pressure, ½ρv² is dynamic pressure, and ρgh is hydrostatic potential energy. In horizontal flow (constant h), as fluid velocity increases through a constricted venturi nozzle, internal static pressure must simultaneously decrease.

Question 14

What is the Reynolds Number (Re) and how does it predict turbulence?

Accepted Answer

The Reynolds Number is a dimensionless ratio of inertial forces to viscous forces in a fluid flow: Re = (ρ × v × D) / μ, where ρ is fluid density, v is velocity, D is pipe diameter, and μ is dynamic viscosity. In circular pipe flow: Re < 2,300 indicates smooth, predictable Laminar Flow; 2,300 < Re < 4,000 is Transitional Flow; and Re > 4,000 indicates chaotic, eddying Turbulent Flow.

Question 15

What is the physical meaning of Einstein’s Mass-Energy Equivalence (E = mc²)?

Accepted Answer

Einstein’s formula E = mc² demonstrates that rest mass is an ultra-dense, concentrated form of energy. Because the speed of light squared (c² ≈ 8.98755 × 10¹⁶ m²/s²) is astronomical, converting just 1 gram (0.001 kg) of mass into pure energy yields E = 0.001 × (2.99792 × 10⁸)² = 8.988 × 10¹³ Joules (~25 million kilowatt-hours or the explosive energy of 21.5 kilotons of TNT).

Constant Name	Symbol	Numerical Value	SI Unit
Speed of Light in VacuumFundamental speed limit of spacetime and electromagnetic wave propagation.	c	299,792,458	m / s
Newtonian Gravitational ConstantProportionality factor in Newton’s law of universal gravitation and Einstein’s Field Equations.	G	6.67430 × 10⁻¹¹	m³ / (kg · s²)
Planck ConstantRelates photon frequency to quantum energy in quantum mechanics (Exact SI Definition).	h	6.62607015 × 10⁻³⁴	J · s
Reduced Planck Constant (h-bar)Quantum of angular momentum: ℏ = h / (2π).	ℏ	1.054571817 × 10⁻³⁴	J · s
Boltzmann ConstantRelates average kinetic energy of particles in a gas with thermodynamic temperature.	k_B	1.380649 × 10⁻²³	J / K
Avogadro ConstantNumber of constituent particles in one mole of any chemical substance.	N_A	6.02214076 × 10²³	mol⁻¹
Elementary ChargeElectric charge carried by a single proton or magnitude of charge on an electron.	e	1.602176634 × 10⁻¹⁹	C (Coulombs)
Electron Rest MassRest mass of a fundamental electron (equivalent to 0.510998950 MeV/c²).	m_e	9.1093837015 × 10⁻³¹	kg
Universal Molar Gas ConstantConstant of proportionality in Ideal Gas Law: R = N_A × k_B.	R	8.314462618	J / (mol · K)
Vacuum Electric PermittivityCapability of vacuum space to permit electric field lines.	ε₀	8.8541878128 × 10⁻¹²	F / m

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