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


> 
> 19. Which of the following orbitals are degenerate in the hydrogen atom with $n = 3$?
>  [![enter image description here](https://i.stack.imgur.com/PbJo4.png)](https://i.stack.imgur.com/PbJo4.png)  
> 
> **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?





> 
> 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.


 5

The one electron of hydrogen, when excited, reaches 3rd energy level and degeneracy is determined by $(n + l)$, where $n$ - energy level, $l = 0$ for $\mathrm{s}$, $1$ for $\mathrm{p}$, $2$ for $\mathrm{d}$, $3$ for $\mathrm{f}$.


 -1

First of all yes there is only 1 e- present in atom of H. But here the atom is "hydrogen like" which can be He+, Li+2 Be3+, etc. The question was twisted at the point n=3, when it said n=3 then the atom can be "hydrogen like" as I mentioned above.


Now n=3 makes the above orbitals with 3s, 3p, 3d and 3f. Now (l) quantum number for **3s=0** for **3p=1**, for **3d=2** and for **3f=3**.


Now, electron can jump in case of **3s=0 to 1, 3p=0 to 3, 3d= 0 to 5 and 3d= 0 to 7**


Thus, we can say that from above orbitals, there will be degeneration in all of them. 


 -3

Ok so the best way to think of this is to compare two atoms. Take for example {Ne} which has 10 electrons so this atom would have a number of n=3. The problem asks what orbitals would be degenerate for n=3 and we know that H has a number of n=1 so this would be just 1s^1 the question is a trick question to make you think that all orbitals above the n=1 orbital are degenerate so really even though it gives you hydrogen its just to throw you off. Picture a n=3 atom for this problem that has no element attached to it in that case all orbitals would be equal energy therefore it would be option E because all orbitals s,p,and d would be degenerate. Hope that helps took my a while to conceptualize this. 


 -4