Which ion of Na+, K+, Mg2+, Ca2+, Rb+ has the smallest radius? Which one
has the largest? Explain the reasons.
The Correct Answer and Explanation is :
The ion with the smallest radius among Na+, K+, Mg²⁺, Ca²⁺, and Rb+ is Mg²⁺, and the ion with the largest radius is Rb+.
Reasoning:
- Ionic Size and Effective Nuclear Charge (Z_eff):
Ionic radii are influenced by two main factors: the effective nuclear charge (Z_eff) and the electron-electron repulsion. Z_eff refers to the net positive charge that an electron experiences from the nucleus, taking into account the shielding effects of other electrons. - Cations and Their Sizes:
All the ions listed (Na+, K+, Mg²⁺, Ca²⁺, and Rb+) are positively charged (cations), meaning they have lost one or more electrons. The loss of electrons results in a decrease in electron-electron repulsion, causing the ion to contract, but the extent of contraction depends on the effective nuclear charge and the number of electrons remaining. - Mg²⁺ (Smallest Radius):
- Magnesium (Mg) has an atomic number of 12 and typically has the electron configuration [Ne] 3s². When it loses two electrons to become Mg²⁺, it attains the electron configuration of neon ([Ne]), with only 10 electrons but still a nucleus with 12 protons.
- The higher charge on the nucleus (12 protons) exerts a strong attractive force on the remaining 10 electrons, pulling them closer. Therefore, Mg²⁺ is very compact, with a small ionic radius.
- Rb+ (Largest Radius):
- Rubidium (Rb) has an atomic number of 37, and its electron configuration is [Kr] 5s¹. Upon losing one electron to form Rb+, it attains the configuration [Kr], but it still has 37 protons attracting only 36 electrons.
- The electron cloud of Rb+ is much larger because the remaining electrons are further from the nucleus due to Rb’s lower Z_eff and the larger size of the atom. Thus, Rb+ has the largest ionic radius.
Trend of Ionic Radii:
The trend of ionic radius is influenced by:
- Charge: Higher charges result in a smaller ionic radius (because the nucleus pulls electrons more tightly).
- Electron Configuration: Ions with more protons relative to the number of electrons tend to have smaller radii because of stronger attraction.
Thus, among the ions, Mg²⁺ has the smallest radius due to its high charge and small electron cloud, and Rb+ has the largest radius because of its lower effective nuclear charge and larger atomic size.