Momentum of intertia for a dihydrogen molecule

In summary, the momentum of inertia for a dihydrogen molecule refers to its resistance to changes in rotational motion. It can be calculated by multiplying the mass of the molecule by the square of its distance from the axis of rotation and is affected by its shape and mass distribution. This property is important in understanding the molecule's behavior and can be influenced by external factors such as temperature and pressure. Compared to other molecules of similar size, dihydrogen molecules have a relatively low momentum of inertia due to their small size and simple linear structure.
  • #1
fab13
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Homework Statement
The rotational energy level of a symmetric molecule like H2 are given by :

##En = n(n + 1)h^{2}/(2J)##

where ##J## is the momentum of inertia of the molecule. Compute the energy of the first rotational level in eV.

the following information is given : distance between the proton in H2: ##74.14 pm##
Relevant Equations
I have used the following equation for momentum of inertia : ##J=MR^{2}## with ##M## the total mass and ##R## the radius of rotation.
I don't know if the value for distance between protons given in the homework is right (##d = 74.14 pm##).

Indeed, on the following link : https://brainly.in/question/7147660 , they take a distance equal to ##d = 4\times10^{-10} m##.

In all cases, the same formula is applied : ##J=2\,m_{p}\,(\dfrac{d}{2})^{2} = m_{p}\,d^{2}/2##

Which value for distance between the 2 protons have I to take ? ##74.14## pm or ##4\times10^{-10} m## ?

Thanks for your help.
 
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  • #3
thanks !
 

1. What is the momentum of inertia for a dihydrogen molecule?

The momentum of inertia for a dihydrogen molecule depends on its orientation and the axis of rotation. It can range from 0.5 amu Å2 for rotation around the bond axis to 1 amu Å2 for rotation perpendicular to the bond axis.

2. How is the momentum of inertia calculated for a dihydrogen molecule?

The momentum of inertia is calculated by summing the products of the mass of each atom and the square of its distance from the axis of rotation. This is known as the parallel axis theorem. In the case of a dihydrogen molecule, the axis of rotation is usually taken to be the bond axis.

3. How does the momentum of inertia affect the rotation of a dihydrogen molecule?

The momentum of inertia determines the rotational energy of a dihydrogen molecule. The higher the momentum of inertia, the more energy is required to rotate the molecule. This can affect the molecule's stability and reactivity.

4. How does the momentum of inertia change with different isotopes of hydrogen?

The momentum of inertia will change with different isotopes of hydrogen due to their different masses. For example, deuterium (D) has a mass twice that of hydrogen (H), so the momentum of inertia for a deuterium molecule will be twice that of a hydrogen molecule.

5. Can the momentum of inertia be used to predict the behavior of a dihydrogen molecule?

The momentum of inertia is one factor that can be used to predict the behavior of a dihydrogen molecule, but it is not the only factor. Other factors such as molecular shape, intermolecular forces, and temperature also play a role in determining the behavior of a dihydrogen molecule. Therefore, the momentum of inertia should be considered along with these other factors for a more accurate prediction.

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