We investigated before the possibility of modifying alpha decay rate by the influence of a laser radiation upon a nucleus. We showed that the laser radiation with the extreme achievable intensity slightly modifies the total rate of alpha decay. A different result may be probably obtained if it use synchrotron radiation for the irradiation of an alpha-active nucleus. At present, synchrotron radiation from the third generation synchrotrons has high brilliance, the photon energy may reach 200-300 keV and, in the future, it may be larger. These energies are comparable with nuclear ones and the effect from the influence of the synchrotron radiation upon alpha decay could be more significant. As it turned out, the change of the alpha decay rate of 238 U isotope into the synchrotron radiation field from the third generation synchrotrons will be negligible.