Question

Two values of spin quantum numbers i.e. $+\dfrac{1}{2}$ and $-\dfrac{1}{2}$ represents:
(a) Up and down spin of the electrons respectively
(b) Two quantum mechanics spin states which refer to the orientation of spin of the electron
(c) clockwise and anti-clockwise spin of the electrons respectively
(d) Anti-clockwise and clockwise spin of the electrons respectively.

Answer 1

Hint: The quantum number tells us about the shell, sub-shell, orientation and spin of the electron in an atom and by knowing about these quantum numbers , we can easily identify what the two values of spin quantum number represent. Now answer it.

Complete answer:
By the term orbital, we mean the three-dimensional space around the nucleus where the probability of finding the electrons is maximum and according to this, the electron can be anywhere in this region and an orbital can accommodate a maximum of two electrons.
Orbitals have different shapes. s orbital is spherically symmetrical, p- orbital is dumbbell -bell shaped etc.
First of all, let’s discuss what a quantum number is. Quantum number tells us that the electron in an atom can be characterized by the four numbers which are known as the quantum numbers which are designated as n, l, m and s. Here, n represents the principal quantum number, l is the azimuthal quantum, m is the magnetic quantum number and s is the spin quantum number.
The quantum number n indicates the energy level which an electron occupies and tells us about the shell to which the electron belongs. The shell with n=1 is called first shell, n=2 is called second shell and so on.
The quantum number l indicates= about the subshell to which an electron belongs and tells us about the shape of the orbital. If l=0, it is spherical shaped(s-orbital)
L=1, it is dumble-bell shaped (p-orbital)
L=3, it is double dumbbell-shaped (d-orbital)
L=4, it has complex shape (f-orbital)
The quantum number m indicates=about the orientation of the electron in the presence of the magnetic field and for each value of l, it has values ranging from -l to 0 to +l.
The quantum number s indicates= about the spin orientation of the electron and the electron-spin can be either in clockwise or anticlockwise direction i.e. $\pm \dfrac{1}{2}$ .
So, the two values of spin quantum numbers i.e. $+\dfrac{1}{2}$and $-\dfrac{1}{2}$ represents the two-quantum mechanics spin which refers to the orientation of spin of the electron.

Hence, option (b) is correct.

Note: The two electrons in an orbital can never have the same value of the spin quantum number , if one electron is having positive value of spin quantum number i.e. as $+\dfrac{1}{2}$, then the second electron will have the negative value of the spin quantum number as $-\dfrac{1}{2}$.