XI.II Units And Measurements

Multiples and Sub-multiples:

nano	micro	milli	centi	deci	deca	hecto	kilo	Mega	Giga	Tera
-9	-6	-3	-2	-1	1	2	3	4	5	6

Some Important Constants: The values of these constants are generally given in question papers. It is important to know their application, which we discuss in different chapters.

• Constant of gravitation, G = 6.67 x 10^-11 Nm²/kg²
• Speed of light in vacuum, c = 2.99 x 10⁸ m/s
• Avagadro constant, N = 6.022 x 10²³ mol^-1
• Gas constant, R = 8.314 JK^-1mol^-1
• Boltzmann constant, k = 1.38 x 10^-23 J/K = 8.614 x 10^-5eV/K
• Stefan-Boltzmann constant, σ = 5.67 x 10 ^-8 Wm^-2K^-4
• Wein's displacement law constant, b = 2.89 x 10^-3 mK
• Charge of proton, e = 1.6 x 10^-19 C
• Mass of electron, m_e = 9.1 x 10^-31 kg = 5.48 x 10^-3 u
• Mass of neutron, m_n = 1.67 x 10^-27 kg
• Permeability of vacuum, μ₀ = 4 π x 10^-27 Tm/A 
• Permittivity of vacuum, ε₀ = 8.854 x 10^-12 Wb A^-1 m^-1
• Faraday constant, F = 96485.3
• Planck constant, h = 6.626 x 10^-34 J s = 4.1357 x 10^-34 eV s
• Rydberg constant, R = 1.097 x 10^-7 m^-1
• Ground state energy of hydrogen atom = 13.6 eV
• Bohr radius, a₀ = 5.29 x 10^-11 m
• Electron-charge to mass ratio, e/m_e = 1.759 x 10^-11 c/kg

Some more constants

• Mechanical equivalent of heat, J = 4186  J/cal
• Standard atmospheric pressure, 1 atm = 1.013 x 10⁵ Pa
• Absolute zero, 0 K = 237.15 ° C
• Electron volt, 1eV = 1.602 x 10^-27J
• Unified Atomic mass unit, 1u = 1.661 x 10^-27 kg
• Electron rest energy, m_ec² = 1.661 x 10^-27 kg
• Energy equivalent of 1 atomic mass unit = 931.5 MeV
• Volume of ideal gas (0 °C, 1 atm), V = 22.4 L
• Acceleration due to gravity, g = 9.78 m/s²

Greek Alphabets:

alpha Α α beta Β β gamma Γ γ delta Δ δ epsilon Ε ε zeta Ζ ζ eta Η η theta Θ θ

iota Ι ι kappa Κ κ lambda Λ λ mu Μ μ nu Ν ν xi Ξ ξ omicron Ο ο pi Π π

rho Ρ ρ sigma Σ σ/ς tau Τ τ upsilon Υ υ phi Φ φ chi Χ χ psi Ψ ψ omega Ω ω

SI Units: Many of the units are named on the names of scientists

Fundamental quantities;

• Length: meter (m)
• Mass: kilograms (kg)
• Time: seconds (s)
• Charge: coulomb (C)
• Luminous intensity: candela (Cd)
• Temperature: kelvin (K)

Derived quantities;

• Current: ampere (A)
• Force: newton (N)
• Work/Energy: joule (J)
• Power: watt (W)
• Potential: volt (V)
• Frequency: hertz (Hz)
• Resistance: ohm (Ω)
• Magnetic flux: weber (Wb)
• Inductance: henry (H)
• Capacitance: farad (F)

Mathematical Formulas: These important formulas should be known for the subject

• Quadratic formula; ax² + bx + c = 0 has solutions x = (-b ± √D)/2a, where D = √(b² - 4ac)
• Binomial Theorem; (1 + x)ⁿ  = 1 + nx +.. if  x<<1
• Product of vectors; 
• Trigonometric Identities;
• Derivatives and Integrals;
• Cramer's rule;