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Two atoms will interact via electrical forces between their protons and electrons. To put them at a distance 
from one another (measured from nucleus to nucleus), a certain amount of energy 
is required, and the minimum energy occurs when the atoms are in equilibrium,
forming a molecule. Often a fairly good approximation to the energy is the Lennard-Jones expression
from one another (measured from nucleus to nucleus), a certain amount of energy is required, and the minimum energy occurs when the atoms are in equilibrium,
forming a molecule. Often a fairly good approximation to the energy is the Lennard-Jones expression
![E(r)=k\left [ \left ( \frac{a}{r} \right )^{12}-2\left ( \frac{a}{r} \right )^6 \right ]](/system/files/resource/33/33298/33786/media/eqn-img_42.gif)
where 
and 
are constants. Note that, as proved in To infinity — and beyond!, the rule that the derivative of 
is 
also works for 
. Show that there is an equilibrium
at 
. Verify (either by graphing or by testing the second
derivative) that this is a minimum, not a maximum or a point of inflection.
and are constants. Note that, as proved in To infinity — and beyond!, the rule that the derivative of is also works for . Show that there is an equilibrium
at . Verify (either by graphing or by testing the second
derivative) that this is a minimum, not a maximum or a point of inflection.
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