Final answer:
The emission of an alpha particle decreases the atomic number by two and the mass number by four, beta particle emission increases the atomic number by one without changing the mass number, and gamma ray emission does not affect either the atomic number or the mass number.
Step-by-step explanation:
When a nucleus emits an alpha particle (symbolized by the Greek letter α or He), which is composed of two protons and two neutrons, the atomic number decreases by two and the mass number decreases by four. This is because the nucleus loses two protons (changing the element) and generally four units of atomic mass (two protons and two neutrons). For instance, when uranium-238 undergoes alpha decay, it transforms into thorium-234, with the atomic number dropping from 92 to 90, and the mass number from 238 to 234.
In the case of beta particle emission (symbolized by the Greek letter β), there is a conversion of a neutron into a proton within the nucleus, which increases the atomic number by one but leaves the mass number unchanged. This form of decay results in one element changing into another in the periodic table due to the change in the number of protons. Gamma ray (γ-ray) emission, however, typically accompanies alpha or beta decay and does not change the atomic number or mass number since it's a form of electromagnetic radiation without mass.