## Unit – I C |

## Definitions of Fundamental Units in S. I. System:

### 1 metre:

- The unit of length is a metre.
- The distance travelled by electromagnetic waves in the vacuum in 1/299, 792, 458 seconds.
- Its symbol is ‘m’.
- Note that the denominator is the velocity of light in the vacuum which is in m/s and is known accurately.
- The wavelength of light is used for defining the standard of length because the wavelength of light is precisely defined in terms of electron transition in an atom, is easily reproducible and is not affected by the change in place, time, temperature and pressure etc.

### 1 kilogram:

- The unit of mass is kilogram.
- 1 kilogram is defined is total mass of 5.0188 × 10
^{25}atoms of C12 isotopes of carbon. Or The mass of a cylinder made up of platinum-iridium alloy kept at International Beuro of Weights and Measure is defined as 1 kilogram. - Its symbol is ‘kg’.

### 1 second:

- The unit of time is second.
- 1 second is a time duration of 9,192,631,770 periods of radiation corresponding to the transition between two hyperfine levels of the ground state of the Cesium-137 atom.
- Its symbol is ‘s’.
- Any happening which repeats itself after regular intervals can be used to measure time.
- Period of vibration of the atom of Cesium – 137 is used for defining the standard of time because the period of vibration of the atom of Cesium – 137 are precisely defined, is easily reproducible and is not affected by a hange in place, time, temperature and pressure etc.

### 1 degree kelvin:

- The unit of temperature is degree kelvin.
- 1 degree kelvin is a fraction 1/ 273.16 of the thermodynamic temperature of the triple point of the water. The triple point of the water is a temperature at which ice, water and water vapour are in equilibrium.
- Its symbol is ‘K’.

### 1 candela:

- The unit of luminous intensity is candela.
- 1 candela is luminous intensity in the normal direction of a surface of area 1/600000 m
^{2}of a black body at the freezing point of platinum under pressure of 1.01325 × 10^{5}N/m^{2}. - Its symbol is ‘cd’.

### 1 ampere:

- The unit of electric current is the ampere.
- 1 ampere is the constant current, which is maintained in each of two infinitely long straight parallel conductors of a negligible cross-section, situated one metre apart in vacuum, will produce between the conductors a force of 2 × 10
^{-7}N/m. - Its symbol is ‘A’.

### 1 kilomole:

- The unit of amount of substance is kilomole.
- 1 mole is the amount of substance which contains as many elementary entities (atoms, molecules, ions, electrons etc.) as there are atoms in 0.012 kg of pure C12. The number of entities in one mole is 6.02252 X 10
^{23}. It is called as Avagadro’s number. - Its symbol is ‘mol’

### 1 radian:

- The unit of plane angle is radian
- One radian is defined as the angle subtended at the centre of a circle by an arc equal in length to the radius of the circle.
- Its symbol is ‘rad’

### 1 steradian:

- The unit of solid angle is steradian
- One steradian is defined as the solid angle that encloses a surface on the sphere of an area equal to the square of its radius.
- Its symbol is ‘sr’

### Other Importnat Units (Not Part of S.I. System):

- 1 fermi or femtometer (F) = 10
^{-15}m - 1 angstrom (A
^{0}) = 10^{-10}m - 1 micron or micrometer = 10
^{-6}m - 1 X-ray unit = 10
^{-13}m - Light year: It is defined as a distance travelled by light in vacuum in one year. 1 light year = 9.46 x 10
^{15}m - One astronomical unit: It is a mean distance between the sun and the earth. 1 AU or 1 astronomical unit = 1.496 x 10
^{11}m - 1 parsec: It is the distance at which an arc of length one astronomical unit subtends an angle of 1 second of an arc. 1 parsec or parallactic second = 3.086 x 10
^{16}m - Note that light year (ly) and parsec (pc) are units of distances and not of time.
- One a.m.u.: It is defined as 1/12 th of mass of one atom. 1 a.m.u. = 1.66 x 10
^{-27}kg

## Some Derived Units