Final answer:
Copper ions Cu²+ and Cu+ are smaller than the neutral copper atom Cu due to the decrease in electron-electron repulsion and an increase in effective nuclear charge. Potassium (K) is the largest among the listed species because it is further down the periodic table. The order from smallest to largest is: Cu²+, Cu+, Cu, K.
Step-by-step explanation:
The question asks us to order copper (Cu), potassium (K), and copper ions (Cu²+ and Cu+) from smallest to largest in size. Atom and ion sizes are influenced by the number of electrons and the effective nuclear charge.
Generally, cations (positively charged ions) are smaller than their neutral atoms because the loss of electrons results in a decreased electron-electron repulsion, allowing the electrons to be pulled closer to the nucleus. Additionally, the more positive the charge of an ion, the smaller its radius due to a greater effective nuclear charge pulling on fewer electrons.
Cu²+ (smallest) - It has lost two electrons and has the greatest effective nuclear charge among the species listed.
Cu+ - With one electron lost, it is larger than Cu²+ but smaller than the neutral Cu atom.
Cu - The neutral copper atom is larger than its cations because it has more electron-electron repulsion without an increase in nuclear charge.
K (largest) - Potassium is larger than copper and its cations due to it being further down the periodic table reflecting its larger atomic size.