The correct option is **C. have high effective nuclear charges**. ### Detailed Explanation: 1. **Understanding Ionization Energy**: - Ionization energy is the energy required to remove an electron from an atom in its gaseous state. Elements with high ionization energies require a significant amount of energy to remove an electron, indicating that their electrons are held tightly by the nucleus. 2. **Effective Nuclear Charge (Z_eff)**: - The effective nuclear charge is the net positive charge experienced by an electron in a multi-electron atom. It accounts for the actual nuclear charge (the total number of protons in the nucleus) and the shielding effect caused by other electrons. - The formula for effective nuclear charge can be approximated as: \[ Z_{\text{eff}} = Z - S \] where \( Z \) is the atomic number (number of protons) and \( S \) is the shielding constant (which represents the extent to which inner electrons shield the outer electrons from the nucleus). 3. **Why High Ionization Energies Correlate with High Z_eff**: - Elements with high ionization energies typically have a high effective nuclear charge. This means that the protons in the nucleus exert a strong attractive force on the outermost electrons, making it more difficult to remove them. - For example, noble gases like helium and neon have high ionization energies because they have a full valence shell and a high effective nuclear charge, which keeps their electrons tightly bound. ### Analysis of Other Options: - **A. Lose electrons easily**: - This option is incorrect because elements with high ionization energies do not lose electrons easily. In fact, they require a lot of energy to remove an electron, which is the opposite of "losing electrons easily." Elements that lose electrons easily typically have low ionization energies. - **B. Have large atomic radii**: - This option is also incorrect. Generally, elements with high ionization energies tend to have smaller atomic radii. A smaller atomic radius means that the outer electrons are closer to the nucleus, which increases the effective nuclear charge felt by these electrons and thus increases ionization energy. - **D. Have low atomic numbers**: - This option is misleading. While some elements with low atomic numbers (like helium) have high ionization energies, this is not a general rule. Many elements with low atomic numbers (like alkali metals) have low ionization energies. Therefore, this statement does not accurately describe the relationship between atomic number and ionization energy. ### Summary of Key Points: - **High ionization energy** indicates that an element holds its electrons tightly due to a strong effective nuclear charge. - **Effective nuclear charge (Z_eff)** is the net positive charge experienced by outer electrons, influenced by the number of protons and the shielding effect of inner electrons. - Elements with high ionization energies typically have **small atomic radii** and do not lose electrons easily. - The relationship between atomic number and ionization energy is not straightforward; low atomic numbers do not guarantee high ionization energy. This understanding of ionization energy and effective nuclear charge is crucial for predicting the behavior of elements in chemical reactions and their placement in the periodic table.