Friday 17 April 2015

Which orbitals of the hydrogen atom are degenerate for n=3?





  1. Which of the following orbitals are degenerate in the hydrogen atom with $n = 3$? enter image description here
    A. II and III only;
    B. I and IV only;
    C. I, II, and IV only;
    D. II, III, and IV only;
    E. all.



The answer says its E. All of them.



First of all isn't there only 1 electron in hydrogen? And how could the $\mathrm{s}$ orbital be degenerate? Doesn't degenerate mean there are multiple places pairs of orbitals can be?



Answer




First of all isn't there only 1 electron in hydrogen?



yes



And how could the s orbital be degenerate? Doesn't degenerate mean there are multiple places pairs of orbitals can be?



"degenerate" means having the same energy. "Degenerate" refers to a set of orbitals. It doesn't make sense to say one orbital is degenerate.



Solving the non-relativistic Schrodinger equation, all the orbitals for a given "n" are degenerate. Energy only depends upon n.


More complete consideration including relativity, spin and quantum electrodynamics shows that they are not all degenerate however.


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