Question

The force constant of 14N
16O is 1550 N m
1
: (6)
(i) Predict its bond order.
(ii) Calculate the reduced mass.
(iii) What is the fundamental frequency in cm1
?
(iv) What will be the fundamental frequency if the O atom is isotopically labeled
as 18O?

Answer 1

Reduced mass = μ = m1 * m2 /(m1 + m2) = 14*16/(14+16) = 112/15 u
                               = 1.239 * 10⁻²⁶ kg

fundamental frequency = f = 1/2π  *√(k/μ)
  = 1/2π *√(1550/1.239*10⁻²⁶) = 5.629 *10¹³ Hz
   = 5.629 * 10¹³ Hz / (3 * 10⁸ m/s) = 1.876 * 10⁵ m⁻¹ = 1876 cm⁻¹

Bond Order = [number of bonding electrons - number of antibonding electrons]/2
                    = [ (2 from N + 4 from O) - (1 from N) ] /2
                    = 2.5
Nitrogen has a bond order of 3 in N2,  O2 has a bond order of 2 in O2.  NO bond has 2.5 as bond order.

If O¹⁸ isotope is used in NO bond, then:
         μ = 63/8 amu = 1.307 * 10⁻²⁶ kg
         f = 1.826  cm⁻¹   (wave number of vibration)