Why energy distribution of beta particle is continous?
I assume you are referring to beta-decay. In this type of decay, an electron (sometimes called beta minus particle, but positron decay is also possible) is emitted. Until the process was understood well enough, it was assumed that there was only an electron leaving the atom. The consequence by kinematics was, that the electron could only have a very sharp energy value. But in experiments it turned to be continuous and always less than expected. So there was a misconception of what was really happening, as the law of conservation of energy seemed to be violated. To solve this problem, Pauli postulated the existence of another particle, now called the neutrino, in order to solve this problem. The missing energy would be taken away by the kinetic energy of the neutrino. This postulated particle was found 30 years later. So to keep it short: It´s continuous because there is another particle emitted together with the electron, a neutrino, so that both of them can carry away any arbitrary fr