  The Geiger-Nuttall (GN) law relates the partial $\alpha$-decay half-life with
the energy of the escaping $\alpha$ particle and contains for every isotopic
chain two experimentally determined coefficients. The expression is supported
by several phenomenological approaches, however its coefficients lack a fully
microscopic basis. In this paper we will show that: 1) the empirical
coefficients that appear in the GN law have a deep physical meaning and 2) the
GN law is successful within the restricted experimental data sets available so
far, but is not valid in general. We will show that, when the dependence of
logarithm values of the $\alpha$ formation probability on the neutron number is
not linear or constant, the GN law is broken. For the $\alpha$ decay of
neutron-deficient nucleus $^{186}$Po, the difference between the experimental
half-life and that predicted by the GN Law is as large as one order of
magnitude.
