Question

Select the correct statement for energy level n=9 Each of the d orbitals have different energy b) All three p orbitals have the same energy because they are degenerate The two s orbitals have the same energy because they are degenerate d) There are a total of 81 electrons at n=9

Answer 1

Solution:

For any given energy level,n (principal quantum number) of an atom there may exixts there are some combinations of orbitals. They are of different shapes, denoted by a letter (s, p, d, f, g,....etc.).

Among them except s orbitals which exists as only one rest are composed of three and more and are considered as degenrate as they are of same or similar energies.

The number of orbitals per level is given by n2 while the maximum number of electrons in a given level is obtained from 2n2.

Coming to the question we can easily cancel out options (a), (c) and (d)

Maximum number of electrons for n=9 is ( 2*92 )= 162 . So option (d) is wrong.

Option (c) is also wrong as ns orbitals cannot be degenerate with respect to themselves.

Also there are 5 degenerate d orbitals in each level so the option (a) is wrong.

Option (b) is correct as there are three p orbitals of exactly same energy which makes them degenerate.

Below a tabular representation of Orbitals and Electron Capacity of the First Four Principle Energy Levels

Principle energy level (n)	Type of sublevel	Number of orbitals per type	Number of orbitals per level(n2)	Maximum number of electrons (2n2)
1	s	1	1	2
2	s	1	4	8
p	3
3	s	1	9	18
p	3
d	5
4	s	1	16	32
p	3
d	5
f	7