Question

Select the correct statement(s) among the following:
(i) Total number of orbitals in a shell with principal quantum number '$n$' is $n^2$.
(ii) Total number of subshell in the $n$th energy level is $n$.
(iii) The maximum number of electrons in a subshell is given by the expression $(4l+2)$.
(iv) $m=l+2$, where $l$ and $m$ are azimuthal and magnetic quantum numbers.

• A. (i), (iii) and (iv) are correct
• B. (i), (ii) and (iii) are correct
• C. (ii), (iii) and (iv) are correct
• D. (i), (ii) and (iv) are correct

Answer 1

Answer: (B)

(i), (ii) and (iii) are correct

The statements (i), (ii) and (iii) are correct.
(i) Total number of orbitals in a shell with principal quantum number 'n' is $n^2$.
Thus, for $n=1$, the number of orbitals $=1^2=1$. It includes 1s orbital.
For $n=2$, the number of orbitals $=2^2=4$. It includes 2s, $2p_x$, $2p_y$ and $2p_z$ orbitals.
For $n=3$, the number of orbitals $=3^2=9$. It includes 3s, $3p_x$, $3p_y$, $3p_z$ $d_{xy}$,$d_{xz}$,$d_{yz}$, $d_{x^2-y^2}$ and $d_{Z^2}$ orbitals.
(ii) Total number of subshell in the nth energy level is n
Thus, for $n=1$, only 1 subshell is present. It includes s orbital.
For $n=2$, two subshells are present. It includes s and p orbitals.
For $n=3$, three subshells are present. It includes s, p and d orbitals.
(iii) The maximum number of electrons in a subshell is given by the expression $(4l+2)$
Thus, s subshell with $l=0$ has $(4l+2)=\left(4\right(0)+2)=2$ electrons.
p subshell with $l=1$ has $(4l+2)=\left(4\right(1)+2)=6$ electrons.
d subshell with $l=2$ has $(4l+2)=\left(4\right(2)+2)=10$ electrons.
f subshell with $l=3$ has $(4l+2)=\left(4\right(3)+2)=14$ electrons.
(iv) $m=-l,....-1,0,+1,.....+l$, So $m=2l+1$ where l and m are azimuthal and magnetic quantum numbers
Thus when $l=3$
$m=-3,-2,-1,0,+1,+2,+3$
Thus, there are 7 values of m. $2l+1=2\left(3\right)+1=7$