Quantum Harmonic Oscillator

[koolcats4life]

Homework Statement

"Vibrational spectroscopic studies of HCl show that the radiation absorbed in a transition has frequency 8.63*10^13 Hz. Calculate the vibrational frequency of the molecule in this transition."

Homework Equations

E_n=(n+1/2)hv
v=(1/(2pi))(sqrt(k/μ))

The Attempt at a Solution

I know I'm supposed to calculate the energy absorbed in the transition first, so:
E = hv
E = (6.626*10^-34)(8.63*10^13)
E = 5.72*10^-20 J


From here, I guess I'll have to use the equation: E_n=(n+1/2)hv, but what n value(s) do I use? Kind of confused here.

Thanks.

 

[anathema]

Thank you for your question. To calculate the vibrational frequency of the molecule in this transition, you will need to use the formula v=(1/(2pi))(sqrt(k/μ)), where v is the vibrational frequency, k is the force constant, and μ is the reduced mass of the molecule.

To find the value of k, you will need to refer to a table of force constants for HCl. From the table, you can see that the force constant for HCl is approximately 480 N/m.

To find the value of μ, you will need to calculate the reduced mass of the molecule using the formula μ=m1m2/(m1+m2), where m1 and m2 are the masses of the atoms in the molecule. For HCl, the masses of hydrogen and chlorine are approximately 1.00794 u and 35.453 u, respectively. Converting these to kg, we get m1=1.67377*10^-27 kg and m2=5.89696*10^-26 kg. Plugging these values into the formula, we get μ=1.66669*10^-27 kg.

Now, we can plug in the values for k and μ into the formula v=(1/(2pi))(sqrt(k/μ)). This gives us a vibrational frequency of approximately 8.63*10^13 Hz, which matches the frequency given in the forum post.

I hope this helps you understand how to calculate the vibrational frequency in this transition. Let me know if you have any further questions.