Question

Number of all subshell of $(n + l) = 7$ is
A. $4$
B. $5$
C. $6$
D. $7$

Answer 1

We know that subshells are the group of an orbital so there exists $4$ subshells which are $s,p,d$ and $f$ subshells. Here $n$ is the Principle quantum number and $l$ is the Azimuthal quantum number where if $n = 1$ then $l$ will be equal to $n - 1$ . for example if $n = 1$ then $l$ will be $0$ which means the subshell will be $1s$ as for azimuthal quantum number $0,1,2,3 \,and\, 4$ are designated as $s,p,d\,and\, f$ respectively.

Complete answer:
In this we need to assign such values to $n$ and $l$ that when we add the two, the sum is $7$

$n$	$l$	$(n + l)$	$Subshell$
$7 \\\ 6 \\\ 5 \\\ 4$	$0 \\\ 1 \\\ 2 \\\ 3$	$7 \\\ 7 \\\ 7 \\\ 7$	$7s \\\ 6p \\\ 5d \\\ 4f$

Here we cannot proceed further to $n = 3,l = 4$ as the value of $l$ should always be less than the value of $n$ so there are only four subshells possible in this case.

**Hence the correct answer will be Option A.

Additional information: **
The values which are used to describe the energy levels of atoms and molecules are known as the quantum numbers. There are four types of quantum numbers present which are the principle quantum number $(n)$-describes the energy level, the azimuthal quantum number $(l)$-describes the subshell , the magnetic quantum number $(m)$- describes the orbital of the subshell and the spin quantum number $(s)$ which describes the spin of the electron .

Note:
There is also an alternative method to solve the question:
We know that $(n + l) = 7$ $- (i)$
Also, we know $l = n - 1$ $- (ii)$
On substituting equation $(i)\& (ii)$ we get: -
$n + n - 1 = 7$
So, $2n = 7 + 1$
$\Rightarrow 2n = 8 \\\ \Rightarrow n = \dfrac{8}{2} \\\ \Rightarrow n = 4$
Hence by this method also we got the possible number of subshells that would be present for the condition $(n + l) = 7$
Also, to find the maximum number of electrons present in a subshell we use the formula: $2{n^2}$