?A simple pair distribution function has the form\(g(r)=1+\cos \left(\frac{4

Chapter 14, Problem P14C.1

(choose chapter or problem)

A simple pair distribution function has the form

\(g(r)=1+\cos \left(\frac{4 r}{r_{0}}-4\right) \mathrm{e}^{-\left(r / r_{0}-1\right)}\)

for \(r \geq r_{0}\) and g(r)=0 for \(r<r_{0}\). Here the parameter \(r_{0}\) is the separation at which the Lennard-Jones potential energy function (eqn 14B.12) \(V=4 \varepsilon\left\{\left(r_{0} / r\right)^{12}-\left(r_{0} / r\right)^{6}\right\}\) is equal to zero.

(a) Plot the function g(r). Does it resemble the form shown in Fig. 14C.1?

(b) Plot the virial \(v_{2}(r)=r(\mathrm{~d} V / \mathrm{d} r)\).

Text Transcription:

g(r)=1+cos(4r/r_0 -4) e^{-(r/r_0-1)

r geq r_0

r<r_0

r_0

V=4 varepsilon{r_0/r)^12-(r_0/r)^6}

v_2(r)=r(dV/dr)