The separation distance at which the energy of the molecule is minimum.

Question

One description of the potential energy of a diatomic molecule is given by the Lennard–Jones potential, U = (A)/(r12) - (B)/(r6)where A and B are constants and r is the separation distance between the atoms. For the H2 molecule, take A = 0.124 x 10-120 eV ⋅ m12 and B = 1.488 x 10-60 eV ⋅ m6. Find (a) the separation distance r0 at which the energy of the molecule is a minimum and (b) the energy E required to break up theH2 molecule.

Answer 1

Question

Chapter 42, Problem 3P

(a)

To determine

The separation distance at which the energy of the molecule is minimum.

(b)

To determine

The energy required to break up the H2 molecule.

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One description of the potential energy of a diatomic molecule is given by the Lennard–Jones potential, U = (A)/(r12) - (B)/(r6)where A and B are constants and r is the separation distance between the atoms. For the H2 molecule, take A = 0.124 x 10-120 eV ⋅ m12 and B = 1.488 x 10-60 eV ⋅ m6. Find (a) the separation distance r0 at which the energy of the molecule is a minimum and (b) the energy E required to break up theH2 molecule.

One model for the potential energy of a two-atom molecule, where the atoms are separated by a distance r, is U(r) = Uo[(¹) ¹2 – ( )²] where ro = 0.8 nm and U₁ = 6.1 eV. Note: 1 eV = 1.6 × 10-19 J. Some helpful units: [Force] = eV/nm [Energy] = eV [distance] = nm Equilibrium Distance What is the distance between the atoms when the molecule is in stable equilibrium? Click here for a hint T'eq Hint: Hint: Hint: Hint: Hint: Hint: Force If the distance between the atoms increases from equilibrium by r₁ = 0.35 nm, then what is the force from one atom on the other associated with this potential energy? (Enter your answer as postive if they repel each other, and negative if they attract.) Fr(req+r₁) Hint: Hint: 0.89105934nm Kinetic Energy Hint: The atoms are oscillating back and forth. The maximum separation of the atoms is r₂ = 2 nm. What is the kinetic energy of the atoms when they are separated by the equilibrium distance? Click here for a hint K(req) Hint: Hint: = -1.288eV/nm 3.99eV

One model for the potential energy of a two-atom molecule, where the atoms are separated by a distance r, is U(r) = U₁[(¹)¹² – ()] where ro = 0.8 nm and ₹₁ = 6.1 eV. 19 Note: 1 eV = 1.6 × 10-¹⁹ J. Some helpful units: [Force] = eV/nm [Energy] = eV [distance] = nm Equilibrium Distance What is the distance between the atoms when the molecule is in stable equilibrium? Click here for a hint req Hint: Hint: Hint: Hint: Hint: Force If the distance between the atoms increases from equilibrium by r₁ = 0.35 nm, then what is the force from one atom on the other associated with this potential energy? (Enter your answer as postive if they repel each other, and negative if they attract.) Fr(req+r₁) Hint: 0.89105934nm Hint: