1. Complete the table we started making in class. i. e. consider all n = 2 states of the hydrogen atom. In the presence of an external magnetic field B, list the total energies of each state in terms of E₀ (13.6 eV), μ_B (the Bohr magneton), and B. Count up the number of different energies allowed.

2. What are the physical differences between a H atom in a 2s, m_s=1/2 state and one in a 4d, m_l = 1, m_s = -1/2 state in the a) absence or b) presence of an external magnetic field?

Some hints for question 2: Since you are asked for physical differences, I would concentrate on the energy of the states (dominated by n) as well as the various aspects of angular momentum (and energy) implied by l, m_l, and m_s. I would only analyze the square of the wavefunction (probability) in terms of r because we haven't talked much about its shape in terms of θ and φ. Actually, you should realize that |ψ|² is constant in φ. The behavior of |ψ|² with θ is important in chemistry. If interested, there is a brief description of the θ behavior in the latter half of section 7.6. You can also try out the "atom in a box" software.