Question

For a shell of principal quantum number $n = 4$, there are:
A.16 orbitals
B.4 subshells
C.32 electrons (maximum)
D.4 electrons with $l = 3$

Answer 1

Hint: The electronic configuration of an atom is represented in its orbitals. An orbital is basically designated by three quantum numbers, $n:$ Principal quantum number, $l:$Azimuthal quantum number and ${m_l}:$Magnetic quantum number.

Complete step by step answer:
The principal quantum number $\left( n \right)$is a positive integer. It determines the size and energy of the orbitals. We know that the size of energy shells increases with increasing $n$. Thus we can say that the orbital size also increases with $n$.
Azimuthal quantum number $\left( l \right)$is an integer having all values between $0$and $n - 1$. It is known as a subsidiary quantum number and is used to represent a subshell. The azimuthal quantum number is also used to define the shape of an orbital.
We know that, each value of $l$is designated with letters as, $s\left( {l = 0} \right),p\left( {l = 1} \right),d\left( {l = 2} \right),f\left( {l = 3} \right)$ and so on.
Magnetic quantum number $\left( {{m_l}} \right)$is an integer having values between $ - l$ to $ + l$ including zero. It gives information about the orientation of an orbital with respect to the coordinate axis..
The number of orbitals in a subshell is given by the number of possible orientations of an orbital.
Thus, we can also say that the number of orbitals in a subshell is equal to the number of values taken by ${m_l}$, which is equal to $2l + 1$.
Thus, since we know that, $n = 4$ thus, we can say that, $l = 0,1,2,3$
This implies that there are 4 subshells.
We know that number of orbitals$ = 2l + 1$
Thus, we can write the total number of subshells$ = 1 + 3 + 5 + 7 = 16$.
According to Pauli’s exclusion principle, an orbital can contain two electrons and hence the maximum number of electrons is 32.
For $l = 3$, number of orbitals$ = 2l + 1 = 7$
Thus, it can accommodate a total of 14 electrons.

Therefore, the correct options are A, B and C.

Note:
The principal quantum number can also be used to calculate the number of orbitals and the maximum number of electrons in a shell.
Number of orbitals$ = {n^2}$ And the maximum number of electrons$ = 2{n^2}$