The Lennard-Jones potential function is a (relatively) simple way to describe th

Question

The Lennard-Jones potential function is a (relatively) simple way to describe the potential energy of
molecular bonds, as a function of separation between the atoms involved. It is often given in the form
PE = A/r^12 - B/r^6 , where A and B are values that depend on the atoms involved. For a hydrogen
molecule, the values are A = 1.95 eV * Å^12 and B = 5.94 eV * Å^6 , where eV is electron-Volt (which is
a small unit of energy (1eV = 1.6 × 10^19J) , and Å is Angstrom, which is a small unit of distance
(1Å = 10^10m) , both of which are commonly used in molecular physics. Given these quantities, for a
hydrogen molecule, what is the equilibrium separation between hydrogen atoms, and what is the
potential energy at that separation?

6) The Lennard-Jones potential function is a (relatively) simple way to describe the potential energy of molecular bonds, as a function of separation between the atoms involved. It is often given in the form --12- , where A and B are values that depend on the atoms involved. For a hydrogen 12 6 molecule, the values are A = 1.95 el' * and B = 5.94e* , where el' is electron-Volt (which is a small unit of energy (1er-1.6 x 10-19), and is Angstrom, which is a small unit of distance (IA -101°m), both of which are commonly used in molecular physics. Given these quantities, for a hydrogen molecule, what is the equilibrium separation between hydrogen atoms, and what is the potential energy at that separation?

Explanation / Answer

At equilibrium potential is minimum.

dPE/dr = 0

-12Ar^-13 + 6Br^-7

Br^6 = 2A

r = (2A/B)^(1/6)

= (2*1.95/5.94)^(1/6)

= 0.932 Å answer

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