Solution: The formula for calculating the energies of an

Chapter 8, Problem 8.98

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The formula for calculating the energies of an electron in a hydrogenlike ion is given in 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 2 ), where Z is the atomic number and is a positive dimensionless quantity called the shielding constant. Consider the helium atom as an example. The physical significance of is that it represents the extent of shielding that the two 1s electrons exert on each other. Thus, the quantity (Z 2 ) is appropriately called the effective nuclear charge. Calculate the value of if the first ionization energy of helium is 3.94 3 10218 J per atom. (Ignore the minus sign in the given equation in your calculation.)