Lennard-Jones Potential V(r) (Condensed Matter)

[Lavace]

http://www.ph.qmul.ac.uk/phy108/CM2005_week2_Lecture3_Interatomic%20Forces2.pdf
Page 6, I've understood all of the notes so far. But it just randomly goes into this, what/where did these p's and q's come from? What do they mean?

Can't find anything that I can understand online!

 

[Redbelly98]

It is found (experimentally, I think) that the potential between atoms or ions has the behavior given by the 1st equation on page 6, where p and q are integer exponents in that expression. That's pretty much it, they are just the exponents that describe the potential. For two neutral, inert gas atoms, p=12 & q=6 describes the potential. For an ion + neutral atom, p and q will be something else. For two oppositely charged ions, we know that q=1 because of the inverse-square-law for charged particles.

Hope that helps.