Question

If the quantum number $1$ has a value $2$, what are the permitted values of the quantum number $m$?
A. $-2,-1,0,1,2$
B. $0,1,2,3,4$
C. $0,1,2$
D. $-1,0,1$

Answer 1

Quantum number refers to a particular character of electron in an atom. They give an idea about location, energy, shape, orientation and spin of electrons in atoms. Different quantum numbers are $\left( n,\ell ,m,s \right)$
$n=$ principal quantum number
$\ell =$ azimuthal quantum number
$m=$magnetic quantum number
$s=$spin quantum number

Formula used:
$-\left( 2\ell +1 \right)$

Complete step by step answer:
Let's take a look at Azimuthal and Magnetic quantum number azimuthal quantum number $\left( \ell \right)$ tell about the number of subshells present in main shell $\left( subshells-s,p,d,f \right)$, tells the shape of various subshells
$\ell =0\to$ s-subshell
$\ell =1\to$ p-subshell
$\ell =2\to$d-subshell
$\ell =3\to$f-subshell
Magnetic quantum numbers $\left( m \right)$ describe the orientation or distribution of electron clouds.
For each value of $'\ell '$ the magnetic quantum number $'m'$may assume all integral values from $-1$ to $+1$ including zero, i.e, total $(2\ell +1)$
Thus, when $\ell =0$, $m=0(1)$(only one value or single orientation in space)
$\ell =1$, $m=3$(it means $3$ orientations in space)
and so on,

So from above we can conclude that the correct answer for this question is $'A'$.

Note: Different values of $'m'$ for a given value of $'\ell '$ provide the total number of ways in which a particular subshell in presence of magnetic field can be arranged in space. along $x,y$ and $z$.
Apart from number of orbits principal quantum also help to define the no of subshell into the shells and whose value is equal to $n.$