The correct answer is option 4 which states that neither the mass number nor the atomic number of the nucleus changes in the gamma decay of a nucleus.

Gamma decay is a type of radioactive decay where a high-energy photon called a gamma ray is emitted from the nucleus of an atom. Unlike alpha and beta decay, which involve the emission of particles from the nucleus, gamma decay only involves the release of electromagnetic radiation.

In gamma decay, the nucleus remains unchanged in terms of its mass number (the total number of protons and neutrons) and atomic number (the number of protons). The emission of a gamma ray does not result in the creation of new particles or the transformation of existing particles within the nucleus.

It`s important to note that while gamma decay does not alter the mass number or atomic number of the nucleus, it can occur alongside other types of radioactive decay such as alpha or beta decay, which do result in changes to these properties.