  The work is dedicated to the development of the electron-lattice energy
exchange theory in metal particles and it dependence of on particle size and
electron temperature. We obtained the expressions for the constants of the
electron-lattice energy exchange using the quantum-kinetic approach for
infinite metal, and compared it with the result of classical kinetic approach.
Both methods give the same result. But for the metal particles smaller than the
mean free path of electrons, as we show, a quantum-kinetic approach (in its
standard form) can not be applied, while the classical approach can be easily
generalized to the particle of such sizes. We found a new peculiarity of the
electron-lattice energy exchange - its temperature dependence around certain
size - "magic size" of metal nanoparticles. Our calculation shown, that this
changes of the electron-lattice energy exchange are associated with alteration
of acoustic subzones which takes part in energy transfer. The change of the
electron temperature can also lead to changes (around the "magic size") in the
acoustic subzones, which are involved in energy transfer. As a result, constant
of the electron-phonon interaction in nanoparticles can be either much higher
or much lower than the corresponding constant for infinite metal.
