Vibrations of a hydrogen molecule

As the temperature increases, the amplitude of the vibrations increase. In summary, the question asks how the rms value of these vibrations will change if one of the hydrogen atoms is replaced with a deuterium atom. The problem may be approached by considering the mass difference between hydrogen and deuterium and its effect on the vibration frequency.
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Homework Statement


Translated from swedish so i hope i get it right...

Observe vibrations along the axis of the bond in a hydrogen molecule (H2). For low temperatueres, by which factor does the rms value ("root-mean-square deviation") of these vibrations amplitude change if one of the hydrogen atoms is changed for a deuterium atom?

My problem is that i don't really know where to begin. So I am not asking for a solution (becasue i know you won't give me one) but a push in the right direction.
 
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  • #2
At low temperatures, the hydrogen molecule will behave as a simple harmonic oscillator. Eg., 2 masses on a linear spring.
 

1. What are the typical vibrational frequencies of a hydrogen molecule?

The vibrational frequencies of a hydrogen molecule depend on the bond length between the two hydrogen atoms. For a stable molecule, the typical frequency range is between 1,000 to 10,000 cm-1.

2. How is the vibrational energy of a hydrogen molecule related to its bond strength?

The vibrational energy of a hydrogen molecule is directly proportional to the bond strength between the two hydrogen atoms. A stronger bond will result in a higher vibrational energy and vice versa.

3. Can hydrogen molecules vibrate in more than one mode?

Yes, hydrogen molecules can vibrate in multiple modes. The number of vibrational modes is equal to the number of atoms in the molecule minus the number of degrees of freedom (3 for a linear molecule and 6 for a non-linear molecule).

4. How do changes in temperature affect the vibrational energy of a hydrogen molecule?

As temperature increases, the vibrational energy of a hydrogen molecule also increases. This is because at higher temperatures, the molecules have more kinetic energy which leads to stronger and more frequent vibrations.

5. Are there any practical applications of studying the vibrations of a hydrogen molecule?

Yes, the study of hydrogen molecule vibrations has several practical applications. It is used in spectroscopy techniques to identify and analyze molecules in various substances. It is also important in understanding chemical reactions and the properties of materials.

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