The accelerative motion of electrons around the nucleus radiates electromagnetic waves that make atoms unstable. In this paper, the differential equation of the radius of electron motion is established on the assumption that an electron moves in a uniform circle around the nucleus for a short time. The trajectory equation of electron in polar coordinate system and the time expression of electron falling to the nucleus are obtained. It is concluded that an electron moves in a spiral around atomic nucleus and falls to the nucleus in about 10-10 s.