In this work, catalytic ignition delay time of combustible gas's small impurities in air on a spherical metal particle of various diameters is analytically determined by the example of gas-air mixtures's flameless combustion with hydrogen impurities on a platinum particle. It is shown that stable flameless combustion is observed after an induction period for particles of a certain range. It has been established that catalytic ignition time of gases is divided into three stages: 1. inert heating, the duration of which still depends on the combustible gas concentration; 2. the stage of self-acceleration and catalyst temperature rise during the course of the catalytic reaction in the transition region; 3. stage of diffusion inhibition and reaching stable catalytic combustion. The characteristic relaxation time was used in a dimensionless form. To determine the duration of the second stage, a modified Frank-Kamenetsky approach is applied. The duration of diffusion inhibition stage in the dimensionless form is practically independent of catalyst particle's diameter, although the catalytic combustion temperature decreases with an increase in the catalyst diameter. Heat transfer by radiation, the role of which increases with the growth of the catalyst size, is included in the effective heat transfer coefficient, which allows maintaining the classical ideology to solving the problem of the induction period.