When using IR spectroscopy, why does a stronger bond have a higher wavenumber?

Answer 1

The wavenumber #tildenu# is related to the force constant:

#\mathbf(tildenu = 1/(2pic)sqrt(k/mu))#

where:

  • #c# is the speed of light, #2.998xx10^(10)# #"cm/s"#.
  • #k# is the force constant in #"kg/s"^2# of the bond between the two atoms in the harmonic oscillator model, which can alternatively be labeled the ball-and-spring model. The force constant value is generally in the hundreds.
  • #mu# is the reduced mass; #mu = (m_1m_2)/(m_1 + m_2)#, where #m_i# is the molar mass of atom #i#.

Since for the same molecule, #mu# remains constant, #c# remains constant, and obviously #2pi# remains constant, for any higher #k#, you can tell that #tildenu# is higher.

A higher force constant #k# means a stiffer "spring" (i.e. stronger bond).

Therefore, a stronger bond has a higher IR frequency when comparing the same type of vibrational motion (e.g. symmetric stretch with symmetric stretch, asymmetric bend with asymmetric bend, etc).

CHALLENGE: Can you show me why the wavenumber frequency for #D_2# for the symmetric stretch is #2990# #cm^(-1)#, whereas that of #H_2# is #4401# #cm^(-1)#? What does that tell you about the bond strength of #H_2# relative to that of #D_2#?

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Answer 2

In IR spectroscopy, a stronger bond has a higher wavenumber because stronger bonds vibrate at higher frequencies, resulting in higher energy transitions and thus higher wavenumbers in the infrared spectrum.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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