The mass of the deuterium molecule D2 is twice that of the hydrogen molecule H2. If the vibrational frequency of H2 is 1.29 × 1014 Hz, what is the vibrational frequency of D2, assuming that the "spring constant" of attracting forces is the same for the two species? Answer in units of Hz.

9.12x10¹³ Hz

Explanation:

The vibrational frequency (ω) of a molecule is given by:

Where:

k: is the spring constant

μ: is the reduced mass

The reduced mass of a diatomic molecule is:

Where ma and mb are the atomic masses of the atoms a and b, respectively, of the diatomic molecule.

Hence, the vibrational frequency of the hydrogen molecule is:

  (1)

From equation (1) we can find k:

   (2)

The vibrational frequency of the deuterium molecule is:

   (3)

By entering equation (2) into equation (3) we can calculate the vibrational frequency of the deuterium molecule:

Therefore, the vibrational frequency of the deuterium molecule is 9.12x10¹³ Hz.

I hope it helps you!