6 תרגיל 2008 רן סלם אטום המימן 1. Show that n electron in the n=2, l=1 state of hydrogen is most likely to be found at r=4a0. a0 is Bohr radios. 2. The radius of the proton is about R0=10-15m, The probability that the electron is inside the volume occupied by the proton is given by P R0 P(r )dr 0 Where P(r) is the radial probability density. Compute P for the hydrogen ground state. (Hint: Show that e 2 r / a0 1 for r R0 is valid for this calculation). צימוד ספין מסילה 3. A hydrogen atom is in the 3D state (n=3, l=2). a. What are the possible values of j? b. What are the possible values of the magnitude of the total angular momentum? c. What are the possible z components of the total angular momentum? 4. Consider a system of two electrons, each with l=1 s=1/2. a. Neglecting spin, what are the possible values of the quantum numbers for the total orbital angular momentum L=L1+ L2? b. What are the possible values of the quantum number S for the total spin S=S1+ S2? c. Using the results of (a) and (b) find the possible quantum numbers j for the combination J=L+S. d. What are the possible quantum numbers j1 and j2 for the total angular momentum of each particle? e. Use the result of (d) to calculate the possible values of j from the combination of j1 and j2. Are this the same as in (c)?