DEGREES OF FREEDOM

DEGREE OF FREEDOM :  

DEGREE OF FREEDOM OF A MOLECULE MAY BE DEFINED AS NUMBER OF INDEPENDENT PARAMETER WHICH MUST BE SPECIFIED TO DESCRIBE THE STATE OR POSITION OF THE MOLECULE COMPLETELY.

SEVERAL DEGREES OF FREEDOM :-

(1)  TRANSNATIONAL DEGREES OF FREEDOM :   SPEED OF A PARTICLE TRAVELLING IN THREE DIMENSION CAN BE EXPRESSED IN TERMS OF THREE COMPONENT ALONG THE THREE PERPENDICULAR AXIS.

(2) ROTATIONAL DEGREES OF FREEDOM :  THIS INDICATES THE ROTATION OF MOLECULES ABOUT THE AXES. 

(3) VIBRATIONAL DEGREES OF FREEDOM  :  IT INDICATES THE VIBRATIONAL OF MOLECULE ABOUT THE STATIONARY CENTRE  OF MASS.

MONO-ATOMIC  MOLECULES   :-

EXAMPLES - He , Ne , Ar

THESE MOLECULES HAVE ONLY TRANSLATIONAL  DEGREES OF FREEDOM AS IT MOVE ALONG THE 3 PERPENDICULAR AXES  x,y,z   DIRECTION .

THUS THEY HAVE 3 TRANSLATIONAL DEGREES OF FREEDOM.  THEY DON'T HAVE ROTATIONAL AND VIBRATIONAL DEGREES OF FREEDOM. 

DIATOMIC MOLECULES(LINEAR MOLECULE)    :-

    EXAMPLE  :  HYDROGEN , SO, CO                                                                                                      ALONG WITH 3 TRANSLATIONAL DEGREE OF FREEDOM ,DIATOMIC MOLECULES CAN ROTATE WITH RESPECT TO 2 PERPENDICULAR AXES WHICH CAN BRING THE CHANGE IN THE POSITION OF ATOMS OF THE MOLECULES . BUT THE AXIS WHICH PASSES THROUGH THE NUCLEI (CALLED INTER NUCLEAR AXIS) DOESN'T BRING ANY CHANGE IN POSITION . SO THERE ARE 2 ROTATIONAL DEGREES OF FREEDOM .

NOW ,THE TWO ATOMS OF THE MOLECULE CAN VIBRATE WITH RESPECT TO THE BOND LENGTH . THUS THEY HAVE ONLY ONE TRANSLATIONAL DEGREES OF FREEDOM.

SO TOTAL DEGREES OF FREEDOM OF DIATOMIC MOLECULES ARE                                                                                                   = 6

SOME EASY FORMULAE TO CALCULATE

(1)  TOTAL DEGREES OF FREEDOM = 3N       (N = NUMBER OF ATOMS IN THE MOLECULE)

(2)  VIBRATIONAL DEGREES OF FREEDOM =                                                                                                        -> LINEAR POLY ATOMIC MOLECULES  =  3N -5                                                                               -> NON LINEAR POLYATOMIC MOLECULES = 3N-6

EQUIPARTION  OF ENERGY :-

TOTAL ENERGY OF A MOLECULE IS DIVIDED EQUALLY AMONG THE DIFFERENT DEGREES OF FREEDOM . BUT  HERE THE DEGREES OF FREEDOM MEANS THE NUMBER OF SQUARED TERMS REQUIRED TO EXPRESS THE TOTAL ENERGY OF MOLECULE.

WILL BE UPDATED ...

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