  An expansion of energy characteristics of wide thin slab of thickness L in
power of 1/L is constructed using the free-electron approximation and the model
of a potential well of finite depth. Accuracy of results in each order of the
expansion is analyzed. Size dependences of the work function and electronic
elastic force for Au and Na slabs are calculated. It is concluded that the work
function of low-dimensional metal structure is always smaller that of
semi-infinite metal sample.
  A mechanism for the Coulomb instability of charged metal clusters, different
from Rayleigh's one, is discussed. The two-component model of a metallic
cluster yields the different critical sizes depending on a kind of charging
particles (electrons or ions). For the cuboid clusters, the electronic spectrum
quantization is taken into account. The calculated critical sizes of
Ag_{N}^{2-} and Au_{N}^{3-} clusters are in a good agreement with experimental
data. A qualitative explanation is suggested for the Coulomb explosion of
positively charged Na_{\N}^{n+} clusters at 3<n<5.
