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)?