Energy (kJ/mol) 4 2 0 -2 02 4 6 8 10 12 14 r (Å) ELJ = 4€ ((÷)¹² - (9)°) For neutral atoms and molecules with a zero charge and no significant dipole moment, the van der Waals interactions are the leading contributions to intermolecular interactions. However, they also contribute to interactions between charged ions and polar molecules in addition to the stronger electrostatic interactions. For distances r approaching 0, the (#) 12 term quickly diverges towards positive infinity, describing repulsions between the electron clouds of the atoms. For small distances rit dominates the -(÷) 6 term, which diverges towards negative infinity for r approaching 0, but is smaller in magnitude. Therefore, the total potential goes to positive inifinity for r approaching 0. 6 However, for increasing distances r the (÷) 12 term very quickly approaches 0. The negative - (=) term also approaches zero for increasing r, but it does so much slower than the positive (÷) 12 term. Therefore, the sum of both terms switches from positive values for small distance r, to negative values with increasing r. The potential then describes a single minimum at negative energies before approaching zero for increasing r. The Lennard-Jones potential contains two parameters, and σ, which are specific to the particular pair of interacting atoms. A formal analysis of the Lennard-Jones potential reveals the meaning of these parameters with respect to characteristic features of the potential. Assume the following numerical values for the parameters to answer the following questions: 1.0391 kJ/mol € σ = 3.415 Å Hint: To make your life easier, derive symbolic expressions for your answers first, then substitute the parameters by their numerical values. Warning: no numerical erros are allowed in this exercise! Your answer must be as exact as possible (don't let that scare you, though).

need help undestanding how to set up step by step please A-B please and thank you

Part A - crossing the x-axis

Part complete

At what distance r=r₀ does the Lennard-Jones potential cross the x-axis in the figure above, i.e. E_LJ(r₀)=0? (provide your answer with 4 significant figures)

r₀ =

3.415

ÅÅ

Part B - Energy minimum

At which distance r_min is the potential energy minimum located? (provide your answer with 4 significant figures)

Part C - Minimum energy

What is the potential energy E_LJ(r_min) in the minimum of the Lennard-Jones potential? (provide your answer with 5 significant figures)

Energy (kJ/mol)
4
2
0
-2
02
4 6 8
10 12
14
r (Å)
ELJ = 4€ ((÷)¹² - (9)°)
For neutral atoms and molecules with a zero charge and no significant dipole moment, the van der Waals interactions are the leading contributions to intermolecular interactions. However, they also contribute to interactions between charged ions and polar molecules in
addition to the stronger electrostatic interactions.
For distances r approaching 0, the (#) 12 term quickly diverges towards positive infinity, describing repulsions between the electron clouds of the atoms. For small distances rit dominates the -(÷) 6 term, which diverges towards negative infinity for r approaching
0, but is smaller in magnitude. Therefore, the total potential goes to positive inifinity for r approaching 0.
6
However, for increasing distances r the (÷) 12 term very quickly approaches 0. The negative - (=) term also approaches zero for increasing r, but it does so much slower than the positive (÷) 12 term. Therefore, the sum of both terms switches from positive
values for small distance r, to negative values with increasing r. The potential then describes a single minimum at negative energies before approaching zero for increasing r.
The Lennard-Jones potential contains two parameters, and σ, which are specific to the particular pair of interacting atoms. A formal analysis of the Lennard-Jones potential reveals the meaning of these parameters with respect to characteristic features of the
potential.
Assume the following numerical values for the parameters to answer the following questions:
1.0391 kJ/mol
€
σ = 3.415 Å
Hint: To make your life easier, derive symbolic expressions for your answers first, then substitute the parameters by their numerical values.
Warning: no numerical erros are allowed in this exercise! Your answer must be as exact as possible (don't let that scare you, though).

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