Finding binding energy from equilibrium bond length

[llabesab16]

1. The equilibrium bond length of the He dimer is 2.97 angstroms. What is the binding energy in kJ/mol for this dimer? Would be dimer be stable at room temperature T= 300K (Hint: compare the binding energy to kT)



2. interaction potential for the dimer:

V(r) = (B/r^13)-(C/r^6), where B= 9.29 x 10^4 kJ(angstrom^13)(mol^-1) and C= 97.7 kJ (angstrom^6)(mol^-1)




3. I didn't know what to do. My guess was to plug the equilibrium bond length into the interaction potential equation, but this gave me a negative answer. I figured that my answer couldn't be negative if I had to compare the binding energy to kT. Any help would be greatly appreciated.

Thanks!

 

[Borek]

Perhaps negative binding energy tells you something about stability?

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methods

 

[Blueshift5]

I would like to offer some guidance on how to approach this problem. First, it is important to understand the concept of binding energy and how it relates to the equilibrium bond length and stability of a dimer. The binding energy is the amount of energy required to break apart the dimer into its individual atoms. This energy is typically measured in kJ/mol and is an indication of the strength of the bond between the two atoms.

To find the binding energy, we can use the given information about the equilibrium bond length and the interaction potential. The interaction potential is a mathematical representation of the attractive and repulsive forces between the two atoms in the dimer. By plugging in the given values for B and C, we can calculate the potential energy at the equilibrium bond length of 2.97 angstroms.

Next, we need to convert this potential energy into binding energy. This can be done by subtracting the potential energy at the equilibrium bond length from the potential energy at an infinite distance (where the two atoms are not interacting). This will give us the binding energy in kJ/mol.

Now, we can compare this binding energy to kT, where k is the Boltzmann constant and T is the temperature in Kelvin. This comparison will give us an indication of the stability of the dimer at room temperature (300K). If the binding energy is significantly higher than kT, then the dimer is considered to be stable at room temperature.

In conclusion, to find the binding energy for the He dimer and determine its stability at room temperature, we need to use the given information about the equilibrium bond length and the interaction potential. By plugging in the values and converting the potential energy into binding energy, we can compare it to kT and determine the stability of the dimer. I hope this helps clarify the problem for you.