Question

What are all the possible values for a (total amgular momentum quantum number) for an electron found in the ap quantum states. Also find the magnitude of s. Then draw all possible total angular momentum distribution in 13-dimensionally. You need to put coordinates. for intercepts on a axis as well as x asis and Y axis cif necessary). The magnitude of orbitals needs to be scated properly.

Answer 1

For an electron in 4p-subshell, S = 1/2 and L = 1

Therefore, J = L + S = 1 + 1/2 = 3/2

|L⃗ | = {L(L+1)}^1/2 h/2$\pi$ = {1(1+1)}^1/2 * 6.625*10^-34 J.s/2*3.14 = 1.49*10^-34 J.s

Now, |S⃗ | = {S(S+1)}^1/2 h/2$\pi$ = {1/2 (1/2 + 1)}^1/2 * 6.625*10^-34 J.s/2*3.14 = 9.13*10^-35 J.s

And |J⃗ | = {J(J+1)}^1/2 h/2$\pi$ = {3/2 (3/2 + 1)}^1/2 * 6.625*10^-34 J.s/2*3.14 = 3.954*10^-34 J.s

Now, the diagram can be drawn as follows.

J z J L+S L Jy Jx