Question

Why does vibrational fundamental frequency decreases with the increase in

masses of bonding atoms? Explain with suitable examples.​

Answer 1

Fundamental vibrational frequency(v)=$\frac{1}{2\pi }$×$\sqrt{\frac{k}{u}) }$----(1)

where

force constant(Bond strength)

μ=Reduced mass of vibrating bonding atoms.

μ=$\frac{m_{1}*m_{2}  }{m_{1}+m_{2}  }$

Here m1 and m2 are the mass of two bonding atoms

Considering equation 1 it is clear that with increasing mass of bonding atom reduced mass increases and fundamental vibrational frequency decreases

so it is inversely proportional to square root of reduced mass of atoms.

Example:

1)F-H(4000)$cm^{-1}$

2)cl-H(2890)$cm^{-1}$

3)Br-H(2650)$cm^{-1}$

since the reduced mass(μ)=Br-H>cl-H>F-H&m1:Br>cl>F