During the present century due to an increase in the number of people on the earth's globe and with a growth of material culture technological and energetic processes have begun to take place which have started to alter the nature of the whole globe. Some of these changes have become so significant as to constitute a danger for the safe existence of humanity as a whole. In this paper it is shown that global problems usually develop according to exponential laws when an acceleration of the processes acquires the character of an explosion. The solution of global problems consists of bringing them under control and preventing an explosion. One of the problems is associated with the depletion of energy resources which are a basic factor determining the level of contemporary civilization. It is shown that the only way to escape the crisis consists of making a transition to atomic energy. An examination is made of the technical, scientific and social diffuclties which lie in the path to this solution and which it is necessary to resolve.