Question

Which quantum number defines the orientation of the orbital in the space around the nucleus?
(A) Principal quantum number $\left(n\right)$
(B) Angular momentum quantum number
(C) Magnetic quantum number $\left(m_l\right)$
(D) Spin quantum number $\left(m_s\right)$

Answer 1

Hint: The relationship between electrons and the nucleus can be explained with the help of four numbers termed as Quantum Numbers. The energy is described by Principal quantum number, shape by Angular momentum quantum number, orientation of the orbital by Magnetic quantum number and spin of electron by the Spin quantum number.

Complete Step By Step Answer:
The four quantum numbers are Principal, Azimuthal or Angular momentum, Magnetic and Spin quantum numbers.
The principal quantum number specifies the distance of the orbital from the nucleus. The farthest electron has values of $n$ as the highest. As we know the electron contains negative charge, so those which are closer to the nucleus are more strongly attracted and bound than those which are farther away. And they are even more stable. We can say that by increasing the value of $n$ , the energy of the electron also increases and it also becomes unstable. The atomic orbitals with the same $n$ collectively are termed as a shell. $n$ is the integer value, i.e. $\left(1,2,3,etc\right)$ .
The angular momentum quantum number which is also known as azimuthal quantum number, tells the shape of the orbital. It can be represented either by a number or a letter. $s$ orbitals are spherical in shape, $p$ orbitals are dumbbell-shaped, $d$ orbitals are double dumbbell-shaped and are very hard to visually represent.
Magnetic quantum number describes the orientation of the orbital in space. In other terms, $m$ indicates that the orbital lies along the $x-$ , $y-$ or $z-axis$ on a three-dimensional graph with a nucleus at the origin. $m$ can take on any value from $-l$ to $l$ . The magnetic quantum number indicates that there may be up to one $s$ orbital, three $p$ orbitals, five $d$ orbitals and so on for each value of $n$ .
Spin quantum number represents the direction of the electron’s spin. It is not dependent on the $n$ , $l$ and $m_l$ . The value of $m_s$ tells in which direction the electron is spinning. The values of the electron spin quantum number are $+{\displaystyle \frac{1}{2}}$ and $-{\displaystyle \frac{1}{2}}$ . The positive value of $m_s$ shows upward spin and negative value shows downward spin.
Thus from the above definition, it is clear that the orientation of the orbital in space is described by magnetic quantum number.
Therefore, option $\left(C\right)$ is correct.

Note:
The main use of quantum numbers is that they help to determine the electron configuration of the atom and also their location in the atom. It also helps us to identify other characteristics of atoms like atomic radius and ionization energy.