According to Maxwell electromagnetic theory , through which path an electron should fall into the nucleus in Rutherford's atomic model:
The Rutherford's model described the atom as a tiny, dense, positively charged core called a nucleus, in which nearly all the mass is concentrated, around which the light, negative constituents, called electrons, circulate at some distance, much like planets revolving around the Sun.According to the model electron’s speed will keep reducing as the electron keeps giving off energy by emitting EM waves and the radius of its rotation will keep decreasing and it will soon crash into the nucleus. If radius is continuously decreasing the electron should follow spiral path according to Maxwell theory.