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What is the reason behind alpha particle giving line spectra and beta particle giving continuous spectra?
(To notify this question had already been asked on this site. Yet, I am not quite clear with its explanation. I wish someone could answer it in simple language without much of mathematics involved.)

Lamichhane88
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    An alpha decay is a two body, a beta decay is a three body decay. We have energy and momentum conservation for both, i.e. there are two equations to satisfy and in the two body problem there are two momenta (the recoiling nucleus and the alpha particle) in the COM system to calculate. This means that the algebraic solution is unique. For the three body beta decay we still have two equations, but three momenta (the recoiling nucleus, the electron and the neutrino) , i.e. the solution is not unique. – CuriousOne Jul 29 '16 at 19:53

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I am assuming you know the model of the nucleus being surrounded by electrons, moving up and down between energy levels over time.

In an slightly similiar way, the neutrons and protons in the nucleus can be visualised as a set of shells, based again around energy levels. A simple alpha decay will release a set amount of energy. This is why you will get a discrete spectrum, as CuriousOne says, it's a two body problem, just the nucleus and the alpha particle.

When a beta particle leaves the nucleus, you have 3 bodies involved, the nucleus, an electron (or positron) and a neutrino. Now there are many more ways the momentum and energy can be shared out, between the 3 bodies, giving rise to a continuous spectrum, due to the laws of conservation of energy and momentum.