3.1 Definition of standard units

  Unit and Dimensions

1. Length $(m)$: The distance traveled by light in vacuum in $\frac{1}{{299,792,458}}$ second is called $1$ metre.

2. Mass $(kg)$: The mass of a cylinder made of platinum-iridium alloy kept at International Bureau of Weights and Measures is defined as $1$ kilogram.

3. Time $(s)$: The second is the duration of $9,192,631,770$ periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of cesium$-133$ atom.

4. Electric current $(A)$: If equal currents are maintained in two infinitely long wires of a negligible cross-section, and held $1\ m$ apart so that the force between them is $2 \times 10^{-7}$ newton per metre of the wires, the current in any of the wires is called $1$ ampere.

5. Thermodynamic temperature $(K)$: The fraction $\frac{1}{273.16}$ of the thermodynamic temperature of the triple point of water is called as Kelvin.

6. Luminous intensity $(cd)$: $1$ candela is the luminous intensity of a blackbody of surface area $\frac{1}{600,000}m^2$ placed at the temperature of freezing platinum and at a pressure of $101,325\ N/m^2$, in the direction perpendicular to its surface.

7. Amount of substance (mol): The mole is the amount of a substance that contains as many elementary entities as there are the number of atoms in $0.012\ kg$ of carbon$-12$.

Two supplementary units in SI system are,

1. Radian (rad): It is defined as the plane angle subtended at the center of the circle, by an arc of the circle equal in length to its radius.

2. Steradian (sr): It is defined as the solid angle subtended at the center of a sphere by an area of the sphere equal to the square of its radius.