The growth rate of the number of neutrons in elements compared to the atomic number varies depending on the region of the periodic table being considered. In general, the ratio of neutrons to protons tends to increase with increasing atomic number, but the rate of increase can vary.
In lighter elements, such as hydrogen, helium, and lithium, the number of neutrons is usually equal to or close to the number of protons. As you move across the periodic table, the number of neutrons generally increases more rapidly than the atomic number.
This is because as the atomic number increases, so does the electrostatic repulsion between protons in the atomic nucleus. The strong nuclear force, which binds protons and neutrons together, helps overcome this repulsion. Neutrons, which are electrically neutral, play a crucial role in stabilizing the nucleus. By increasing the number of neutrons, the strong nuclear force can better counteract the electrostatic repulsion among the protons.
Furthermore, additional neutrons can provide more nuclear binding energy, making the nucleus more stable. This is particularly evident in heavier elements, such as those found in the lanthanides and actinides, where the ratio of neutrons to protons becomes increasingly larger.
It's worth noting that the rate of increase in the number of neutrons compared to the atomic number is not constant throughout the periodic table. There are certain regions, such as the transition metals, where the growth rate of neutrons may not be as significant. However, the overall trend is that as atomic number increases, the number of neutrons tends to grow faster, contributing to the stability of the nucleus.