Final answer:
After beta decay, the tritium nucleus, which contains 2 neutrons and 1 proton, is transmuted into helium-3, with an atomic number that has increased by one.
Step-by-step explanation:
A nucleus of tritium contains 2 neutrons and 1 proton. If the nucleus undergoes beta decay, emitting an electron, the nucleus is transmuted into helium-3. During beta decay, a neutron is converted into a proton, and an electron (beta particle) is ejected from the nucleus. As a result, the mass number remains the same (because the neutron and proton have nearly equal mass), but the atomic number increases by one since there's an addition of a proton. Therefore, the nucleus of tritium (hydrogen-3), after beta decay, becomes a nucleus of helium-3 (with 2 protons and 1 neutron).