Which of the following is the best estimate for the effective nuclear charge (Z_{eff}) experienced by a 4d electron in a silver (Ag) atom?

• A. Z_{eff} \approx 29
• B. Z_{eff} \approx 7.6
• C. Z_{eff} \approx 1
• D. Z_{eff} \approx 47

Answer: (B)

Verified step by step guidance

1. Identify the atomic number (Z) of silver (Ag). Silver has an atomic number of 47, meaning it has 47 protons in its nucleus.
2. Understand that the effective nuclear charge (Z_{eff}) is the net positive charge experienced by an electron after accounting for the shielding effect of other electrons. It can be estimated using Slater's rules or a simplified approach: \(Z_{eff} = Z - S\), where \(S\) is the shielding constant.
3. Determine which electrons contribute to shielding the 4d electron. Electrons in inner shells and electrons in the same shell but different subshells partially shield the nuclear charge. For a 4d electron, consider the electrons in shells with principal quantum numbers less than 4 and the electrons in the 4s and 4p orbitals.
4. Calculate the shielding constant \(S\) by summing the contributions of all shielding electrons according to Slater's rules: for example, electrons in inner shells contribute more to shielding than electrons in the same shell.
5. Subtract the shielding constant \(S\) from the atomic number \(Z\) to find the effective nuclear charge: \(Z_{eff} = Z - S\). This value represents the approximate net positive charge felt by the 4d electron.