what is zero point energy calculate the number of normal modes of vibration for the following compounds (1)PF3 (2) CLNO (3) XeF2
Answers
What is zero point energy? Calculate the number of normal modes of
vibration for the following compounds:
(i) PF3 (ii) ClNO (iii) XeF2
Soution: The vibration energy of a molecule is given by E=(v+1/2)hν
where,v= vibrational quantum number, ν=frequency of vibration of the bond,
At 0 K E0=(1/2)hν ,where, E0=zero point energy.
That means even at 0 K temperature bond is vibrating
In order to describe a point in 3d space we need three co-ordinates. So total degree of
freedom =3.So molecules containing N number of atoms =3N,
Among 3N degrees of freedom there are 3 translational degrees of freedom along co-ordinate
axis and 3 rotational degrees of freedom for non-linear molecules,2 for linear molecules.
Since for linear molecules rotation along its bond axis does not change its co-ordinates.
Therefore ,Total number of vibrational degrees of freedom for linear molecules=(3N-5)
And for non-linear molcules=(3N-6)
(i) PF3:Shape-Trigonal pyramidal(Non-linear)
Therefore ,Total number of vibrational degrees of freedom=(3×4)-6=6
The number of normal modes of vibration=6
(ii)ClNO:Shape: V shaped(Non-linear)
Therefore ,Total number of vibrational degrees of freedom=(3×3)-6=3
The number of normal modes of vibration=3
(iii) XeF2: Shape: Linear
Therefore ,Total number of vibrational degrees of freedom=(3×3)-5=4
The number of normal modes of vibration=4
ans by riyaz