A student, having seen the termination condition , argues: “Since is just and added…
PHYSICS · Multi-part · Fermi University Physics · Quantum Mechanics · Atomic, Molecular & Optical Physics · One-electron atoms and the origins of atomic structure
Quantum Mechanics: From the Photon to the Hydrogen Atom, Ch The hydrogen atom
Problem
A student, having seen the termination condition n=nr+l+1, argues: “Since n is just nr and l added together, the number of radial nodes nr must be the same for every state at a given n, namely nr=n−1, taking l=0 as the baseline.” Test the claim for the hydrogen level n=4, using the eigenvalue relation ∣L∣=l(l+1)ℏ of Chapter 10.
((a)) List the values of l allowed at n=4, and the value of nr each one requires.
((b)) Does every n=4 state have the same number of radial nodes? Answer the claim directly.
((c)) Give ∣L∣, as a multiple of ℏ to three significant figures, for the n=4 state with the most radial nodes, and for the one with the fewest.