Question

The magnetic quantum number represents:
(A) Size of the orbital.
(B) Spin angular momentum.
(C) Orbital angular momentum.
(D) Spatial orientation orbital.

Answer 1

Hint: Magnetic quantum number is required to explain the fact that when the source producing the line spectrum is placed in a magnetic field, each spectral line splits up into a number of lines (Zeeman effect).

Complete answer:
When an electron moves around the nucleus, it generates an electric field. This electric field in turn produces a magnetic field which can interact with the external magnetic field. Thus under the influence of the external magnetic field, the electrons of a subshell can orient themselves in certain preferred regions of space around the nucleus called orbitals. The magnetic quantum number determines the number of preferred orientations of the electrons present in a subshell. Since each orientation corresponds to an orbital, therefore, the magnetic quantum number determines the number of orbitals present in any subshell and hence its spatial arrangement.

Hence, option D is correct.

Additional information :
The magnetic quantum number is denoted by the letter $m$ or $m_l$ and for a given value of $l$ , it can have all the values ranging from $-lto+l$ including zero , that is , $-l,-(l-1),-(l-2)....0,1...(l-2),(l-1),l$ .
Thus, for every value of $l,m$ has $(2l+1)$ values. For example,
(i) For $l=0$ (s-subshell), m can have only one value, that is , $m=0$ . This means that s-subshell has only one orbital called s-orbital.
(ii)For $l=1$ (p-subshell), m can have three values, that is, $m=-1,0,+1$ . In other words, p-subshell has three orientations in space. In other words, a p-subshell has three orbitals.
(iii) For $l=2$ (d-subshell), m can have five values, that is , $m=-2,-1,0,+1,+2$ . This implies that there are five different orientations of d-subshell in space. In other words, d-subshell has five d-orbitals.
(iv) Similarly, when $l=3$ (f-subshell), m can have seven values, that is, $m-3,-2,-1,0,+1,+2,+3$ This implies that there are seven different orientations of the f-subshell. In other words, f- subshell has seven f-orbitals .

Note: Magnetic quantum number also gives the quantized values of the z - component of the angular momentum $(L_z)$ of the electron in an orbital according to the expression:
$L_z=m({\displaystyle \frac{h}{2\pi }})$