Discussion
Degeneracy in rotational levels for H-atom along z-axis for l = 0, 1, 2, 3 are :
(Given : \(\dfrac{\hbar^{2}}{2I}\) = 1.2 × 10−21 J)
Answer: B
The degeneracies are 1, 3, 5, 7.
For angular momentum quantum number l, the projection quantum number ml takes the values −l, ..., 0, ..., +l, so each level is (2l + 1)-fold degenerate:
\[ \begin{aligned} l=0 &: 1,\quad l=1: 3 \\ l=2 &: 5,\quad l=3: 7 \end{aligned} \]
The value of ℏ2/2I fixes the energies, E = l(l + 1)ℏ2/2I, but not the degeneracy. 1, 2, 3, 4 counts l + 1; 2, 4, 6, 8 doubles that; and 1, 4, 9, 16 is (l + 1)2, the degeneracy of the hydrogen shells n = 1 to 4, not of a single l level.
No comment is present. Be the first to comment.
Loading…
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development