Discussion
The angular part of the wavefunction for the electron in a hydrogen atom is proportional to \(\sin^{2}\theta \cos\theta \, e^{2i\phi}\). The values of the azimuthal quantum number (l) and the magnetic quantum number (m) are, respectively
Answer: C
The quantum numbers are l = 3 and m = 2.
The azimuthal factor \(e^{im\phi}\) gives m directly: \(e^{2i\phi}\) means m = +2, not -2.
For l, count the powers of the polar functions. A spherical harmonic \(Y_{l}^{m}\) contains \(\sin^{|m|}\theta\) times a polynomial in \(\cos\theta\) of degree \(l - |m|\). Here \(\sin^{2}\theta\) gives |m| = 2 and the single \(\cos\theta\) gives \(l - 2 = 1\), so l = 3. Indeed \(Y_{3}^{2} \propto \sin^{2}\theta\cos\theta\,e^{2i\phi}\), an f orbital.
An l = 2 function with m = 2 is \(\sin^{2}\theta\,e^{2i\phi}\) with no cosine factor, so the 2 and 2 option fails, and the -2 options have the wrong sign of the exponent.
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