While elements have different atomic numbers, which correspond to the number of protons in their nuclei, it is true that atoms of different elements can have similar sizes. This apparent contradiction can be explained by considering the distribution of electrons within atoms.
In atoms, electrons occupy distinct energy levels or orbitals around the nucleus. These energy levels are characterized by their principal quantum number (n), with higher values of n corresponding to higher energy levels further from the nucleus. Each energy level can accommodate a specific number of electrons: the first energy level (n=1) can hold a maximum of 2 electrons, the second energy level (n=2) can hold a maximum of 8 electrons, and so on.
The size of an atom can be roughly approximated by its atomic radius, which is defined as the distance from the nucleus to the outermost electron shell. Despite differences in atomic number, atoms can have similar atomic radii when they have the same number of occupied electron shells or similar electron configurations.
For example, elements in the same group of the periodic table tend to have similar outer electron configurations, leading to similar atomic sizes. This is known as the periodic trend of atomic radius. For instance, the alkali metals (Group 1) all have a single electron in their outermost energy level, resulting in similar atomic radii.
The similarity in atomic size among elements with different atomic numbers can be mathematically explained by considering the effective nuclear charge experienced by the outermost electrons. The effective nuclear charge is the net positive charge experienced by an electron, taking into account the shielding effect of inner-shell electrons. It is determined by the number of protons in the nucleus and the number of inner-shell electrons.
When the effective nuclear charge experienced by the outermost electrons is similar, the attractive force between the nucleus and the outermost electrons is comparable. As a result, atoms with different atomic numbers can have similar atomic radii.
It's important to note that while atoms of different elements can have similar sizes, there are exceptions and variations based on factors such as electron-electron repulsion, ionization energy, and electron shielding. These factors can influence the atomic radius and result in deviations from the general trends.