Why does lower concentration cause the metal atoms to dissipate more?
It is not primarily that the process $\ce{M(s) -&gt; M^n+(aq) + n e-}$ is faster for more diluted solutions.
The main reason is that the opposite process $\ce{M^n+(aq) + n e- -&gt; M(s)}$ is slower for more diluted solutions.
As the net effect, there is dissolution of $\ce{M^n+(aq)}$ ions and the electrode gaining more negative potential, until the rate of both processes gets equal and the electrode reaches its equilibrium potential.
Because the rate of ion dissolution grows with increased potential,
while the rate of ion depositions grows with decreased potential.
The final effect is, the electrode in then more diluted ion solution has the more negative potential.