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

Hint: 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 \[n.\]