Question

For n= $3$, find the number of subshells?

Answer 1

Orbitals that have the same value of the principal quantum number form a shell. Orbitals within a shell are divided into subshells that have the same value of angular quantum number. Shell and subshell are described with a two-character code such as $2p$ or $4f$.

Complete step-by-step answer:
Azimuthal quantum number (l) designates the subshells to which the electron belongs as well as it also tells the shape of the orbitals. We should also remember that this quantum number is also termed as azimuthal quantum number. The value of azimuthal quantum number (l) is determined by the value of principal quantum number, which is designated by (n)

For given shell the number of subshells can be found using the relation
l = n-$1$
By this formula we can say that for the first shell n=1, there are l= $1-1=0$subshells.
In the question, we are given with the value of n= 3
If we calculate the value of l, for the given subshell we get;
l= n-$1$
l=$3-1=2$

Do not mistake the value of l=$2$by assuming the fact that it contains only two subshells. This means that n=3 contains $0,1,2$all values of subshell. So, if we count then we can say that there are 3 subshells for n=3.

The representation of the subshells for the corresponding values of l is represented in a tabular form below:

‘’n’’ values	‘’l’’ values	Representation of the subshell
$1$	$0$	1s
$2$	$0,1$	2s, 2p
$3$	$0,1,2$	3s, 3p, 3d
$4$	$0,1,2,3$	4s, 4d, 4p, 4f

Here, for n=3 there are 3s, 3p, 3d subshells.

Note: Always be careful while dealing with such problems. The most common area or step at which the students commit mistakes is after the calculation of value of l. in the above problem, l=$2$. Students think there are two subshells but in actuality there are $0,1,2$ all values possible and each value corresponds to a specific representation as seen in the tabular form above.