Solution Found!
Answer: The formula for calculating the energies of an
Chapter 8, Problem 98P(choose chapter or problem)
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 \((Z-\sigma)\), 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 \((Z-\sigma)\) is appropriately called the "effective nuclear charge." Calculate the value of a if the first ionization energy of helium is \(3.94\times10^{-18}~ \mathrm J\) per atom. (Ignore the minus sign in the given equation in your calculation.)
Questions & Answers
QUESTION:
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 \((Z-\sigma)\), 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 \((Z-\sigma)\) is appropriately called the "effective nuclear charge." Calculate the value of a if the first ionization energy of helium is \(3.94\times10^{-18}~ \mathrm J\) per atom. (Ignore the minus sign in the given equation in your calculation.)
ANSWER:Step 1 of 2
From the given,
The atomic number for a helium atom is 
And the principle quantum number 