The effective nuclear charge (Zeff) can be estimated using the ionization energy of an electron in an atom. To find Zeff for the 1s electron in a silver (Ag) atom with an ionization energy of 2,462 x 10⁶ kJ/mol, we can use the following formula:
Zeff = (Ionization Energy in kJ/mol) / (Rydberg Constant in kJ/mol for hydrogen)
The Rydberg constant for hydrogen is approximately 1312 kJ/mol. Therefore, we can plug in the values:
Zeff = (2,462 x 10⁶ kJ/mol) / (1312 kJ/mol) ≈ 1873.67
This number seems excessively high for an effective nuclear charge, which typically is much less than the actual atomic number (Ag has an atomic number of 47). It indicates that while calculations give an approximation, they must be corrected for factors like electron shielding and repulsion in multi-electron atoms.
Thus, although the direct calculation gives us a base estimate, further refinement considering electron shielding mechanisms gives a Zeff value closer to the atomic number but reduced by the screening effect of inner electrons. A better estimate for the 1s electron’s Zeff in silver might approximate around 28-32, as established in more complex calculations.