Final answer:
Potassium (K) is the largest among the listed atoms and ions because it has the most electron shells and experiences the least effective nuclear charge which leads to a larger atomic radius. Cations are smaller than their neutral atoms due to decreased electron-electron repulsion and increased nuclear attraction.
Step-by-step explanation:
The size of an atom or ion is influenced by two main factors: the number of electron shells, and the effective nuclear charge experienced by the electrons. In the given list (K, K+, Ca, Ca2+, Li), potassium (K) is the largest because it has the most electron shells and the least nuclear charge, causing the least attraction towards the nucleus. This makes the electron cloud more spread out and the atomic radius larger.
When comparing ions, a cation (positively charged ion) will be smaller than its neutral atom because the loss of electron(s) leads to a decrease in electron-electron repulsion and allows the nucleus to pull the remaining electrons closer, thereby shrinking the ion. Thus, K+ is smaller than K. Similarly, Ca2+ is smaller than a Ca atom.
Regarding the same charge state, the number of protons also plays a role. Potassium (K), with one positive charge, is larger than calcium (Ca) with two positive charges (Ca2+), because the greater charge on Ca2+ pulls the electrons in more tightly, making the ionic radius smaller. Lithium (Li), having fewer electron shells compared to potassium, is smaller than potassium atoms. Therefore, the order from largest to smallest, disregarding charge, would be: K > Ca > Li. Considering charge, K+ and Ca2+ would be smaller than their respective neutral atoms.