Chapter 8, Problem 8.98QP

The formula for calculating the energies of an electron in a hydrogenlike ion is given in Problem 8.57. This equation cannot be applied to many-electron atoms. One way to modify it for the more complex atoms is to replace Z with (Z − σ), where Z is the atomic number and σ is a positive dimensionless quantity called the shielding constant. Consider the helium atom as an example. The physical significance of σ is that it represents the extent of shielding that the two 1s electrons exert on each other. Thus, the quantity (Z − σ) is appropriately called the “effective nuclear charge.” Calculate the value of σ if the first ionization energy of helium is 3.94 × 10⁻¹⁸ J per atom. (Ignore the minus sign in the given equation in your calculation.)