Why? A radioactive isotope is usually the result of a difference in the number of protons and neutrons, which causes instability within the nucleus of atoms, hence the term nuclear. When an element undergoes radioactive decay, it does so to achieve a more stable nuclide.
Elements that undergo alpha decay (α) lose two protons and two neutrons, or a 42He2+ ion plus energy. This decay helps to bring the neutron to proton ratio down and hence makes the nuclide more stable.
Beta decay occurs in one of two forms, β+ and β-. β- results from having a high ratio of neutrons to protons. It occurs when one of the neutrons in the nucleus splits to form a proton, which remains in the nucleus and an electron, which is emitted at high velocity. In effect for beta minus you lose a neutron gain a proton. A β+ emission occurs when the atom has a low neutron to proton ratio, in this decay a proton splits to form a neutron, which remains in the nucleus, and a positron, this form of decay is not as common as beta minus decay. In effect beta plus decay loses a proton and gains a neutron.
Gamma radiation (γ) is short wave high-energy electromagnetic radiation. A change in the nuclide of the atom does not occur with the release of gamma radiation. Gamma rays are high in energy and are produced from processes such as nuclear fusion and fission or when an electron and a positron come in contact with each other.
With this knowledge the answers can be analyzed to determine if any of the forms of decay would produce a more stable nuclide.
Answering the Question:
To answer this question, it is important to understand what it is that makes an atom radioactive. Answer (1) is the hydrogen isotope tritium (3H), which is an unstable isotope of hydrogen. However, as γ rays do not result in a decrease in the number of neutrons to create a more stable form of hydrogen, γ decay is unlikely.
31H → 31H + γ radiation
Answer (2) is potassium 42 and is said to undergo β+ decay, which involves the loss on a proton and the gaining of a neutron. This would result in Argon 42 being formed, which would probably be less stable that potassium 42.
4219K → 4218Ar + 0+1e (β+ particle)
Answer (3) is nitrogen 16; α decay would result in the loss of two neutrons and two protons, resulting in Boron 12, which would probably be unstable.
167N → 125B + 42He (α particle)
Answer (4) is phosphorous 32; β- decay would result in the loss of a neutron, and the gaining of a proton. This would result in the formation of sulfur 32, which is the naturally occurring form of sulfur, and would, therefore, have a stable nuclide.
3215P → 3216S + 0-1e (β- particle)