Per Atom VS Per Particle

And we test the expression from the post "Photons With Kinetic Energy?" date 5 Dec 2017,

$f=\sqrt{\cfrac{c^3}{8\pi}*{density}*{Z}*3.4354}$

with copper, $Z=29$ and density $8.96\,gcm^{-3}$

$f=\sqrt{\cfrac{c^3}{8\pi}*8960*29*3.4354}=9.7826e14\,Hz$

Copper has a work function of $\Psi=4.65\,eV$, so

$f=\cfrac{\Psi}{h_{\small{eV}}}=\cfrac{4.65}{4.135667516e-15}=1.1244e15\,Hz$

and we are off by $1.15$ times.

For Caesium, $Z=55$ and density $1.93\,gcm^{-3}$

$f=\sqrt{\cfrac{c^3}{8\pi}*1930*55*3.4354}=6.2526e14\,Hz$

Caesium has a work function of $\Psi=2.1\,eV$, so

$f=\cfrac{\Psi}{h_{\small{eV}}}=\cfrac{2.1}{4.135667516e-15}=5.0778e14\,Hz$

and we are off by $0.812$ times.

Not bad...