- Which of the following orbitals are degenerate in the hydrogen atom with $n = 3$?
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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