I would like to know during Nuclear fusion how/why Atomic mass of β becomes zero. For example: two Protons fuse to form a deuterium nucleus. Please see the attachment.

Thanksenter image description here

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    $\begingroup$ A $\beta$ particle is an electron (or in this case a positron), which is 2000 times lighter than a neutron or proton. Thus its mass can be neglected. $\endgroup$ – Clever Mar 12 '15 at 19:33
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    $\begingroup$ Comment to the question (v1): in your equation the term $_2^0\beta$ has charge number $+2$, but the positron has charge $+1$. As written, your relation suggests incorrectly that charge is not conserved. $\endgroup$ – rob Mar 13 '15 at 13:34

The superscript is not mass, it is the mass number $A$ (i.e. the number of nucleons). It is is sometime called the "atomic mass", but that should be understood as a shorthand for "atomic mass number".

A positraon, being a fundamental particle in its own right, has zero nucleons and as such has a mass number of zero.

The notation used there is problematic, however, because a positron does not have a $Z$ of 2. Finally kudos to Bill N for noting that the neutrino has been left out of the final state (though to be fair it generally is in elementary treatments).

Aside directed toward the comments on the question: the positron mass is not negligible as it is about 20% of the energy liberated by the fusion.

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