Problem 65
In studying electron screening in multielectron atoms, you begin with the alkali metals. You look up experimental data and find the results given in the table. The ionization energy is the minimum energy required to remove the least-bound electron from a ground-state atom. (a) The units kJ/mol given in the table are the minimum energy in kJ required to ionize 1 mol of atoms. Convert the given values for ionization energy to the energy in eV required to ionize one atom. (b) What is the value of the nuclear charge \(Z\) for each element in the table? What is the n quantum number for the least-bound electron in the ground state? (c) Calculate \(Z$$_{eff}\) for this electron in each alkali-metal atom. (d) The ionization energies decrease as \(Z\) increases. Does \(Z$$_{eff}\) increase or decrease as \(Z\) increases? Why does \(Z$$_{eff}\) have this behavior?
Problem 66
You are studying the absorption of electromagnetic radiation by electrons in a crystal structure. The situation is well described by an electron in a cubical box of side length \(L\). The electron is initially in the ground state. (a) You observe that the longest-wavelength photon that is absorbed has a wavelength in air of \(\lambda\) = 624 nm. What is \(L\)? (b) You find that \(\lambda\) = 234 nm is also absorbed when the initial state is still the ground state. What is the value of \(n$$^2\) for the final state in the transition for which this wavelength is absorbed, where \(n$$^2\) = \(n$$_X^2\) + \(n$$_y^2\) + \(n$$_z^2\) ? What is the degeneracy of this energy level (including the degeneracy due to electron spin)?
Problem 70
In the Bohr model, what is the principal quantum number \(n\) at which the excited electron is at a radius of 1 \(\mu\)m? (a) 140; (b) 400; (c) 20; (d) 81.
Problem 72
Assume that the researchers place an atom in a state with \(n\) = 100, \(l\) = 2. What is the magnitude of the orbital angular momentum \(L\) associated with this state? (a) \(\sqrt{2} \space\hslash \); (b) \(\sqrt{6} \space\hslash\); (c) \(\sqrt{200}\space \hslash\); (d) \(\sqrt{10,100}\space \hslash \).
