Master10
Units, Measurements & Scientific Instruments Module

Scientific Constants, SI Prefixes & Conversions

Fundamental scientific constants and standardized metric prefixes establish the universal quantitative foundation of physics, chemistry, and metrology. Following the landmark 2019 redefinition of the International System of Units (SI) by the General Conference on Weights and Measures (CGPM), all seven base units are explicitly defined in terms of exact numerical values for seven fundamental physical constants: the caesium ground-state transition frequency, the speed of light in vacuum, Planck's constant, the elementary charge, the Boltzmann constant, the Avogadro constant, and the luminous efficacy of monochromatic radiation. In tandem, fundamental universal constants such as Newton's universal gravitational constant, the Stefan-Boltzmann constant, the Rydberg constant, the fine-structure constant, and the universal gas constant govern gravitational dynamics, quantum energy states, and thermodynamics. The metric decimal system utilizes standardized SI prefixes—expanded at the 27th CGPM in 2022 to encompass scales from quecto (10^-30) and ronto (10^-27) to ronna (10^27) and quetta (10^30)—to express extreme physical magnitudes without ambiguity. Mastery of these constants, metric scales, and dimensional conversion equivalences is essential for rigorous scientific analysis and competitive examination precision.

Key Concepts & Examination Highlights

  • The speed of light in a vacuum (c) is defined as exactly 299,792,458 m/s (2.998 x 10^8 m/s), serving as the defining constant for the SI unit of length (metre).
  • Planck's constant (h) has the exact defined SI value of 6.62607015 x 10^-34 Js (kgm^2*s^-1), defining the SI unit of mass (kilogram) via the Kibble balance.
  • The elementary electric charge (e) is defined as exactly 1.602176634 x 10^-19 Coulombs, serving as the defining constant for the SI unit of electric current (ampere).
  • Boltzmann's constant (k or kB) is defined as exactly 1.380649 x 10^-23 J/K (kgm^2s^-2*K^-1), defining the SI unit of thermodynamic temperature (kelvin).
  • Avogadro's constant (NA or L) is defined as exactly 6.02214076 x 10^23 mol^-1, defining the SI unit of amount of substance (mole).
  • The unperturbed ground-state hyperfine transition frequency of the Caesium-133 atom (Delta nu_Cs) is exactly 9,192,631,770 Hz (s^-1), defining the SI unit of time (second).
  • The luminous efficacy of monochromatic radiation of frequency 540 x 10^12 Hz (K_cd) is defined as exactly 683 lm/W, defining the SI unit of luminous intensity (candela).
  • The Universal Gravitational Constant (G), first experimentally determined by Henry Cavendish in 1798 using a torsion balance, has a CODATA value of approximately 6.67430 x 10^-11 Nm^2/kg^2 (m^3kg^-1*s^-2).
  • The Universal Gas Constant (R = NA k) has an exact calculated value of approximately 8.314462618 Jmol^-1K^-1 (or 0.08206 Latmmol^-1K^-1).
  • The Faraday constant (F = NA * e), representing total electric charge per mole of electrons, has an exact value of approximately 96,485.33212 C/mol.
  • The Stefan-Boltzmann constant (sigma) has a value of approximately 5.670374419 x 10^-8 Wm^-2K^-4.
  • The fine-structure constant (alpha), a dimensionless fundamental constant characterizing the strength of electromagnetic interaction, is approximately equal to 1/137.035999 (approx 7.29735 x 10^-3).
  • The Rydberg constant (R_infinity) for an infinitely heavy nucleus has a CODATA value of approximately 1.0973731568 x 10^7 m^-1.
  • The Bohr radius (a_0), representing the most probable distance between proton and electron in a ground-state hydrogen atom, is approximately 5.291772109 x 10^-11 m (0.529 Angstroms).
  • The rest mass of an electron (m_e) is approximately 9.1093837 x 10^-31 kg (equivalent to rest energy of 0.5109989 MeV).
  • The rest mass of a proton (m_p) is approximately 1.6726219 x 10^-27 kg (938.272 MeV), which is roughly 1836.15 times heavier than an electron.
  • The rest mass of a neutron (m_n) is approximately 1.6749275 x 10^-27 kg (939.565 MeV), slightly exceeding the mass of a free proton.
  • The Unified Atomic Mass Unit (1 u or 1 Dalton), defined as 1/12 the mass of an unbound neutral Carbon-12 atom, is approximately equal to 1.660539066 x 10^-27 kg (931.494 MeV/c^2).
  • The electric permittivity of free space (epsilon_0 or vacuum permittivity) is approximately 8.8541878128 x 10^-12 F/m (C^2N^-1m^-2).
  • The magnetic permeability of free space (mu0 or vacuum permeability) has an experimentally determined CODATA value of approximately 1.256637062 x 10^-6 N/A^2 (H/m), linked by c = 1/sqrt(epsilon0 * mu_0).
  • The characteristic impedance of vacuum (Z0 = sqrt(mu0/epsilon_0)) is approximately 376.7303 Ohms (approx 120*pi Ohms).
  • The Bohr magneton (muB = e*hbar / (2*me)), expressing the magnetic moment of an electron caused by orbital or spin angular momentum, is approximately 9.274010 x 10^-24 J/T.
  • The nuclear magneton (muN = e*hbar / (2*mp)), expressing the intrinsic magnetic dipole moment of nucleons, is approximately 5.050783 x 10^-27 J/T.
  • Wien's displacement constant (b = lambda_max T) equals approximately 2.897771955 x 10^-3 mK.
  • Standard acceleration due to Earth's gravity (g_n or standard g) is internationally defined by CGPM as exactly 9.80665 m/s^2 (32.1740 ft/s^2).
  • Standard atmospheric pressure (1 atm) is defined as exactly 101,325 Pa (101.325 kPa = 1.01325 bar = 760 Torr).
  • The 27th CGPM in November 2022 officially adopted four new SI metric prefixes: Quetta (10^30, Q), Ronna (10^27, R), Ronto (10^-27, r), and Quecto (10^-30, q).
  • The SI prefix Yotta (symbol Y) represents a factor of 10^24, while Zetta (symbol Z) represents a factor of 10^21.
  • The SI prefix Exa (symbol E) represents a factor of 10^18, while Peta (symbol P) represents a factor of 10^15.
  • The SI prefix Tera (symbol T) represents a factor of 10^12, while Giga (symbol G) represents a factor of 10^9.
  • The SI prefix Mega (symbol M) represents a factor of 10^6, while Kilo (symbol k) represents a factor of 10^3.
  • The SI prefix Hecto (symbol h) represents 10^2 (100), Deca (symbol da) represents 10^1 (10), Deci (symbol d) represents 10^-1 (0.1), and Centi (symbol c) represents 10^-2 (0.01).
  • The SI prefix Milli (symbol m) represents 10^-3, while Micro (symbol mu) represents 10^-6.
  • The SI prefix Nano (symbol n) represents 10^-9, while Pico (symbol p) represents 10^-12.
  • The SI prefix Femto (symbol f) represents 10^-15, while Atto (symbol a) represents 10^-18.
  • The SI prefix Zepto (symbol z) represents 10^-21, while Yocto (symbol y) represents 10^-24.
  • One Astronomical Unit (1 AU), defined as the exact mean distance between the Earth and the Sun, is standardized as exactly 149,597,870,700 metres (approx 1.496 x 10^11 m).
  • One Light-Year (1 ly), the distance that light travels in vacuum in one Julian year (365.25 days), is approximately equal to 9.46073 x 10^15 metres (approx 9.46 x 10^12 km or 63,241 AU).
  • One Parsec (1 pc), defined as the distance at which one astronomical unit subtends an angle of one arcsecond, equals exactly (180*3600/pi) AU approx 3.085677581 x 10^16 metres (approx 3.26156 light-years).
  • One Angstrom (1 A) is a non-SI unit of length widely used in atomic spectroscopy and crystallography, defined as exactly 10^-10 metres (0.1 nm).
  • One Fermi (or femtometre, 1 fm), used to measure nuclear radii and subatomic dimensions, equals exactly 10^-15 metres.
  • One Electronvolt (1 eV), defined as the kinetic energy gained by an electron accelerating through an electrostatic potential difference of one volt, equals exactly 1.602176634 x 10^-19 Joules.
  • One Calorie (thermochemical calorie) is defined as exactly 4.184 Joules, while one International Table (IT) calorie equals 4.1868 Joules.
  • One Kilowatt-hour (1 kWh), the commercial unit of electrical energy, equals exactly 3.6 x 10^6 Joules (3.6 MJ).
  • One Horsepower (mechanical or imperial horsepower, 1 hp) is standardized as exactly 550 ft*lbf/s approx 745.69987 Watts (commonly rounded to 746 W), whereas metric horsepower (PS) equals 735.49875 W.
  • One Bar is defined as exactly 100,000 Pascals (10^5 Pa = 100 kPa = 0.1 MPa), slightly less than 1 standard atmosphere (1.01325 bar).
  • One Torr is defined as exactly 1/760 of a standard atmosphere, equivalent to approximately 133.3224 Pascals (1 mm Hg).
  • One Curie (1 Ci), the historical unit of radioactivity named after Marie and Pierre Curie, is defined as exactly 3.7 x 10^10 Becquerels (disintegrations per second).
  • One Roentgen (1 R), a legacy unit of ionizing radiation exposure, is defined as the amount of radiation producing 2.58 x 10^-4 Coulombs of electric charge per kilogram of dry air.
  • One Nautical Mile is internationally standardized as exactly 1,852 metres (1.15078 statute miles), based on one minute of latitude along a meridian, giving a speed of 1 knot (1 nautical mile per hour approx 0.5144 m/s).
Curriculum & Reference Sources: BIPM SI Brochure (9th Edition), CODATA Internationally Recommended Values of Fundamental Physical Constants, and 27th CGPM Resolutions (2022).

Sample Solved Questions & Concept Explanations

8 Verified Concept Questions
Q1.MEDIUM

In the International System of Units (SI), what is the derived unit of electrical capacitance, named after the British scientist who discovered electromagnetic induction?

Q2.HARD

Which non-contact scientific instrument is specially designed to measure extremely high temperatures (such as inside blast furnaces or stars) by detecting emitted thermal radiation?

Q3.EASY

Which precision laboratory instrument is specifically designed to measure the radius of curvature of spherical optical surfaces such as lenses and mirrors?

Q4.EASY

Which medical instrument, consisting of an inflatable cuff and a mercury or aneroid manometer, is used to measure human blood pressure?

Q5.EASY

What is the SI base unit used to measure the amount of substance?

Q6.EASY

What is the SI derived unit of force, named in honour of the English physicist who formulated the laws of motion and gravitation?

Q7.EASY

What is the SI derived unit of energy, work, and quantity of heat?

Q8.EASY

What is the SI derived unit of power, defined as one joule per second?