Yes, elemental metals generally get heavier as their atomic number increases. Atomic number corresponds to the number of protons in the nucleus of an atom, and the mass of an atom is primarily determined by the sum of its protons and neutrons. Since the atomic number increases as you move across a period in the periodic table, the number of protons and neutrons in the nucleus also increases. This leads to an increase in the mass of the atom.
However, it's important to note that the relationship between atomic number and atomic mass is not always strictly linear. The atomic mass of an atom is influenced by other factors such as isotopes, which are atoms of the same element with different numbers of neutrons. Isotopes can have slightly different masses, and their relative abundance in nature can affect the overall atomic mass of an element. Additionally, electron configuration and the arrangement of electrons in different energy levels can also have a small impact on the atomic mass. Nevertheless, as a general trend, elemental metals tend to become heavier as their atomic number increases.