Provide a shell model diagram for \(\mathrm{K}^{+}\) showing all electrons explicitly and then show how the core charge for \(\mathrm{K}^{+}\) was calculated.

Electron configuration is a way of representing the distribution of electrons among the orbitals of an atom. It's vital in understanding chemical reactions and the physical properties of elements. For potassium (K), a neutral atom has 19 electrons. Its ground state configuration is [Ar]4s^1, meaning after the argon core ([Ar]), there's an additional electron in the 4s orbital. Upon losing an electron and becoming a positively charged ion (K^+), its electron configuration mirrors that of argon: 1s^2 2s^2 2p^6 3s^2 3p^6.
This simplication reveals that the valence electron–the one in the highest energy level, which is most involved in chemical bonding–has been removed, leading to a full octet that is energetically stable.

The core charge, also referred to as the effective nuclear charge, is an important concept in chemistry as it explains the attraction force experienced by the valence electrons from the nucleus. To calculate the core charge, use the formula: Core charge = Number of protons - Number of inner shell electrons. For K^+, this calculation is straightforward. Since a potassium ion loses its outermost electron, it has an atomic number of 19 (corresponding to its protons) and 18 inner shell electrons. Consequently, the core charge for a K^+ ion would be 19 - 18 = +1. This positive core charge reflects that there's a single positive charge pulling on the remaining electrons after accounting for the negative charge of the inner electrons.

The potassium ion (K^+) is formed when a neutral potassium atom loses one electron. This results in a cation with a positive charge. It's interesting to note that K^+ has the same electron configuration as argon, a noble gas, which is nearly inert due to having a completely filled valence shell. Hence, a potassium ion has a stable octet, which is energetically favorable and makes it less reactive than its neutral atom form. Understanding this ionization process of potassium and its resulting stability is crucial when delving into chemical reactions and bonding behavior involving K^+.

While core charge calculation provides a theoretical value, the effective nuclear charge is the net positive charge experienced by an electron in a multi-electron atom. It's greatly affected by the shielding effect, which is where inner electrons partially shield outer electrons from the full charge of the nucleus. The effective nuclear charge can be estimated using various rules and calculations, one of which is the core charge formula provided in the exercise. For a potassium ion, this value indicates a single positive charge that influences the electron cloud—a crucial factor in periodic trends like atomic size and ionization energy.

• Effective Nuclear Charge = Z - Shielding,
• where Z is the atomic number and Shielding is the number of inner-shell electrons.

Understanding this effective pulling force on the valence electrons by the nucleus can help explain why elements exhibit particular chemical and physical properties.