General Science Module

SI Units & Fundamental Physical Constants

The International System of Units (SI), maintained by the Bureau International des Poids et Mesures (BIPM), defines seven base physical quantities: meter (length), kilogram (mass), second (time), ampere (electric current), kelvin (thermodynamic temperature), mole (amount of substance), and candela (luminous intensity). In 2019, the General Conference on Weights and Measures (CGPM) implemented a landmark redefinition of SI units, fixing all base units to invariant fundamental physical constants rather than physical artifacts. Key fundamental constants include Planck's constant ( $h = 6.626 \\\\times 10^{-34} \\\\ ext{ J}\\\\cdot\\\\ ext{s}$ ), the speed of light in vacuum ( $c = 299,792,458 \\\\ ext{ m/s}$ ), the elementary electric charge ( $e$ ), and the Avogadro constant ( $N_A = 6.022 \\\\times 10^{23} \\\\ ext{ mol}^{-1}$ ).

Practice Topic MCQs All Category Topics

Key Concepts & Examination Highlights

The 2019 SI redefinition officially tied the kilogram to Planck's constant ( $h$ ) using the Kibble balance, retiring the International Prototype of the Kilogram.
There are seven fundamental base SI units: meter (m), kilogram (kg), second (s), ampere (A), kelvin (K), mole (mol), and candela (cd).
The speed of light in a vacuum is defined as an exact universal constant of 299,792,458 meters per second.
Planck's constant ( $h$ ) is fixed at exactly $6.62607015 \times 10^{-34} \ ext{ J}\cdot\ ext{s}$ , defining the fundamental quantum relationship between photon energy and frequency ( $E = h\nu$ ).
The Avogadro constant ( $N_A$ ) is defined as exactly $6.02214076 \times 10^{23} \ ext{ mol}^{-1}$ , representing the number of constituent particles in one mole of a substance.
The elementary electric charge ( $e$ ) is defined as exactly $1.602176634 \times 10^{-19} \ ext{ C}$ , which defines the base unit ampere (A).
The Boltzmann constant ( $k$ ) is fixed at exactly $1.380649 \times 10^{-23} \ ext{ J/K}$ , linking thermodynamic temperature in kelvins to thermal energy.
The universal gravitational constant ( $G$ ), first measured experimentally by Henry Cavendish in 1798, has an approximate value of $6.674 \times 10^{-11} \ ext{ N}\cdot\ ext{m}^2/\ ext{kg}^2$ .
Derived SI units include the pascal ( $\ ext{Pa} = \ ext{N/m}^2$ ) for pressure, the joule ( $\ ext{J} = \ ext{N}\cdot\ ext{m}$ ) for energy and work, and the watt ( $\ ext{W} = \ ext{J/s}$ ) for power.
Frequency is measured in hertz ( $\ ext{Hz} = \ ext{s}^{-1}$ ), electric capacitance in farads ( $\ ext{F} = \ ext{C/V}$ ), and magnetic flux density in teslas ( $\ ext{T} = \ ext{Wb/m}^2$ ).
Luminous intensity is quantified by the candela (cd), defined by the fixed luminous efficacy of monochromatic radiation of frequency $540 \times 10^{12} \ ext{ Hz}$ .
The meter is defined by taking the fixed numerical value of the speed of light in vacuum $c$ to be $299,792,458 \ ext{ m/s}$ , where the second is defined by the cesium-133 hyperfine transition frequency.
The second is defined by taking the fixed numerical value of the unperturbed ground-state hyperfine transition frequency of the cesium-133 atom ( $\Delta\nu_{\ ext{Cs}}$ ) to be $9,192,631,770 \ ext{ Hz}$ .
The kelvin is defined by setting the fixed numerical value of the Boltzmann constant $k$ to $1.380649 \times 10^{-23} \ ext{ J/K}$ , eliminating reliance on the triple point of water.
The mole is defined by containing exactly $6.02214076 \times 10^{23}$ elementary entities, corresponding to the Avogadro constant ( $N_A$ ).
Radioactivity is measured in the SI derived unit becquerel ( $\ ext{Bq} = \ ext{s}^{-1}$ ), representing one nuclear decay per second, while the older non-SI unit curie (Ci) equals $3.7 \times 10^{10} \ ext{ Bq}$ .
Absorbed radiation dose is measured in grays ( $\ ext{Gy} = \ ext{J/kg}$ ), whereas equivalent and effective radiation doses are measured in sieverts ( $\ ext{Sv} = \ ext{J/kg}$ ).
Magnetic flux is measured in webers ( $\ ext{Wb} = \ ext{V}\cdot\ ext{s}$ ), and magnetic inductance is measured in henries ( $\ ext{H} = \ ext{Wb/A}$ ).
Electrical conductance is measured in siemens ( $\ ext{S} = \Omega^{-1}$ ), which represents the reciprocal of electrical resistance in ohms.
Luminous flux is measured in lumens ( $\ ext{lm} = \ ext{cd}\cdot\ ext{sr}$ ), while illuminance is measured in lux ( $\ ext{lx} = \ ext{lm/m}^2$ ).
Plane angle is measured in radians (rad), while solid angle is measured in steradians (sr), both of which are treated as dimensionless derived SI units.
The gas constant ( $R$ ) is defined as $R = N_A k \approx 8.314462618 \ ext{ J}/(\ ext{mol}\cdot\ ext{K})$ , appearing in the ideal gas equation $PV = nRT$ .
The Stefan-Boltzmann constant ( $\sigma$ ) is approximately $5.670374419 \times 10^{-8} \ ext{ W}/(\ ext{m}^2\cdot\ ext{K}^4)$ , governing total blackbody radiant emittance ( $E = \sigma T^4$ ).
Faraday's constant ( $F = e N_A$ ) is approximately $96,485.33212 \ ext{ C/mol}$ , representing the magnitude of electric charge per mole of electrons.
The permeability of free space ( $\mu_0$ ) and permittivity of free space ( $\varepsilon_0$ ) are related to the speed of light by the exact relationship $c = 1/\sqrt{\mu_0 \varepsilon_0}$ .
The fine-structure constant ( $\alpha = \frac{e^2}{4\pi \varepsilon_0 \hbar c}$ ) is a fundamental dimensionless coupling constant characterizing electromagnetic interaction strength, approximately equal to $1/137.036$ .
The Rydberg constant ( $R_\infty$ ) is approximately $1.097373 \times 10^7 \ ext{ m}^{-1}$ , governing the wavelengths of spectral emission lines of hydrogen in the Rydberg formula.
The Bohr magneton ( $\mu_B = \frac{e\hbar}{2m_e}$ ) is approximately $9.274010 \times 10^{-24} \ ext{ J/T}$ , expressing the magnetic dipole moment of an electron due to its orbital or spin angular momentum.
The nuclear magneton ( $\mu_N = \frac{e\hbar}{2m_p}$ ) is approximately $5.050783 \times 10^{-27} \ ext{ J/T}$ , defining the standard magnetic dipole moment unit for protons and atomic nuclei.
Magnetic field intensity ( $H$ ) is measured in amperes per meter ( $\text{A/m}$ ), whereas magnetic flux density ( $B$ ) is measured in teslas ( $\text{T} = \text{Wb/m}^2$ ).
Kinematic viscosity is measured in meters squared per second ( $\text{m}^2/\text{s}$ ), with the older CGS unit being the stokes ( $\text{St} = 10^{-4} \ ext{ m}^2/\ ext{s}$ ).
Dynamic viscosity is measured in pascal-seconds ( $\text{Pa}\cdot\ ext{s}$ ), where 1 $\text{Pa}\cdot\ ext{s}$ equals 10 poise ( $\text{P}$ ) in the CGS system.
Surface tension is measured in newtons per meter ( $\text{N/m}$ ) or joules per square meter ( $\text{J/m}^2$ ), representing the energy required to increase surface area.
Electric dipole moment is measured in coulomb-meters ( $\text{C}\cdot\ ext{m}$ ), with the historical non-SI chemical unit being the debye ( $1 \ ext{ D} \approx 3.33564 \times 10^{-30} \ ext{ C}\cdot\ ext{m}$ ).
The optical power of a corrective lens is measured in dioptres ( $\text{D} = \text{m}^{-1}$ ), equal to the reciprocal of focal length in meters.
Sound intensity level is measured on a logarithmic scale in decibels (dB), defined as $10 \log_{10}(I/I_0)$ with reference threshold intensity $I_0 = 10^{-12} \ ext{ W/m}^2$ .
One astronomical unit (AU) is defined as exactly 149,597,870,700 meters, representing the mean distance from the Earth to the Sun.
One light-year is the distance traversed by light in a vacuum in one Julian year, equal to approximately $9.461 \times 10^{15}$ meters ( $9.461$ trillion km).
One parsec (pc) is the astronomical distance at which one astronomical unit subtends an angle of one arcsecond, equal to approximately 3.26 light-years or $3.086 \times 10^{16}$ meters.
The solar mass ( $M_\odot$ ) is approximately $1.98847 \times 10^{30} \ ext{ kg}$ , used as a standard celestial unit of mass in astrophysics.
The standard atmosphere (atm) is defined as exactly 101,325 pascals, equivalent to 760 millimeters of mercury (760 Torr) or 1.01325 bar.
The triple point of water, historically used to define the kelvin, occurs at exactly 273.16 K (0.01°C) at a partial vapor pressure of 611.657 pascals.
Absolute zero is 0 Kelvin, equivalent to $-273.15^\circ\ ext{C}$ or $-459.67^\circ\ ext{F}$ , at which classical thermodynamic entropy reaches its minimum value.
The curie (Ci), an older unit of radioactivity named after Marie and Pierre Curie, is defined as exactly $3.7 \times 10^{10}$ disintegrations per second (37 GBq).
The roentgen (R) is a legacy unit of measurement for the exposure of ionizing radiation in air, producing $2.58 \times 10^{-4} \ ext{ C/kg}$ of electrical charge.
Electric conductivity ( $\sigma$ ) is measured in siemens per meter ( $\text{S/m}$ ), while electrical resistivity ( $\rho$ ) is measured in ohm-meters ( $\Omega\cdot\ ext{m}$ ).
Specific heat capacity has the SI unit joule per kilogram-kelvin ( $\text{J}/(\ ext{kg}\cdot\ ext{K})$ ), and thermal conductivity has the SI unit watt per meter-kelvin ( $\text{W}/(\ ext{m}\cdot\ ext{K})$ ).
Mass attenuation coefficient is measured in square meters per kilogram ( $\text{m}^2/\ ext{kg}$ ), quantifying the reduction in ionizing radiation intensity as it penetrates matter.
The electronvolt ( $\text{eV} = 1.602176634 \times 10^{-19} \ ext{ J}$ ) is an energy unit representing the kinetic energy gained by an electron accelerating through an electric potential of one volt.
The SI prefixes span twenty-four orders of magnitude, ranging from quecto ( $10^{-30}$ ) and ronto ( $10^{-27}$ ) to ronna ( $10^{27}$ ) and quetta ( $10^{30}$ ), officially adopted in November 2022.

Curriculum & Reference Sources: Bureau International des Poids et Mesures (BIPM), National Institute of Standards and Technology (NIST), CGPM Resolutions

Sample Solved Questions & Concept Explanations

8 Verified Concept Questions

Q1.EASY

What is the SI unit of Force in physics?

Q2.EASY

What is the approximate speed of light in a vacuum?

Q3.EASY

What is the SI unit of Electric Current?

Q4.EASY

What is the SI unit of Energy, Work, and Heat?

Q5.EASY

What is the SI unit of Frequency of a periodic wave?

Q6.MEDIUM

Which universal physical constant is denoted by 'G' and equals approximately 6.674 × 10^-11 N·m²/kg²?

Q7.MEDIUM

The Avogadro constant (NA), representing the number of particles in one mole of a substance, is equal to what value?

Q8.MEDIUM

The absolute zero temperature on the Kelvin thermodynamic scale corresponds to what temperature on the Celsius scale?