Question

The quantum numbers n = 3, l = 1, m = +1 and $s=+\dfrac{1}{2}$, represent the unpaired electron present in:
(A)- Sodium atom
(B)- Aluminium atom
(C)- Fluorine atom
(D)- Potassium atom

Answer 1

Hint: The set of numbers that are used to describe the position and energy of the electron in an atom are known as quantum numbers. This set of numbers describes the trajectory and movement of an electron in an atom.

Complete step by step answer:
-There are four different types of quantum numbers, which are - Principal quantum number (denoted by ‘n’), Orbital angular momentum quantum number (denoted by ‘l’), Magnetic quantum number (denoted by ‘m’), Electron spin quantum number (denoted by ‘${{m}_{s}}$’).

-Let us now discuss each type of quantum number-
(i) Principal quantum number (n)- This quantum number represents the principal energy level or shell in which the electron revolves around the nucleus. The values for the principal quantum number are always an integer, except 0. The energies of the various principal shells follow the sequence as-
$1<2<3<4<5<...$

(ii) Orbital angular quantum number (l)- This quantum number determines the subshell to which an electron belongs. This quantum number is also known by another name, which is the azimuthal quantum number. The value of this quantum number depends on the value of the principal quantum number and ranges between 0 and (n-1). The values of the orbital quantum number follow the sequence as-
For the first shell, let us say K, n = 1, then ‘l’ will have one value, that is l = 0.
For the second shell, let us say L, n = 2, then ‘l’ will have two values, that is l = 0,1.
For the third shell, let us say M, n = 3, then ‘l’ will have three values, that is l = 0,1 and 3. For the fourth shell, let us say N, n = 4, then ‘l’ will have four values, that is l = 0,1,2 and 3.

(iii) Magnetic quantum number- This quantum number represents the orientation of an atomic orbital in space. This quantum number yields the projections of the angular momentum corresponding to the orbital along a given axis. The value of the magnetic quantum number depends on the value of the azimuthal quantum number and have the total number as (2l + 1) The values of the magnetic quantum number follows the trend-
For s-subshell, l = 0, then m = 0.
For p-subshell, l = 1, then m = -1, 0, +1.
For d-subshell, l = 2, then m = -2, -1, 0, +1, +2.
For f-subshell, l = 3, then m = -3, -2, -1, 0, +1, +2, +3.

(iv) Spin quantum number- This quantum number represents the direction of the spin of the electrons. The spin of the electron can be either in a clockwise direction or in the anti-clockwise direction. The value of this quantum number can be either $+\dfrac{1}{2}or-\dfrac{1}{2}$ .
-Now, we have known about each quantum number in detail. Let us now look at the values of the quantum numbers given to us-
n = 3, l = 1, m = +1 and s$=+\dfrac{1}{2}$.

-From the knowledge we gained so far, we can say that the electron being considered is present in $3{{p}_{x}}$ orbital. So, the electronic configuration of the molecule is $1{{s}^{2}}2{{s}^{2}}2{{p}^{6}}3{{s}^{2}}3p$.

-Since, the electron is unpaired, and all the orbitals before 3p are filled. Now for the value of the principal quantum number (n), the number of electrons are $n=2{{n}^{2}}$.
Therefore, the minimum number of electrons that are present in the system = 2 + 8 + 2 +1 = 13.
So, the correct answer is Aluminium. Other possibilities for the electron to belong can be for Silicon or phosphorus.
So, the correct answer is “Option B”.

Note: Let us now see the significance of the quantum number.
-The principal quantum number describes the most probable distance of the electrons from the nucleus, the larger the value of ‘n’, the farther the electron is from the nucleus, the larger the size of the orbital and hence the larger the atom.
-The azimuthal quantum number gives the shape of an orbital and therefore the angular distribution.
The number of angular nodes present is equal to the value of the angular momentum quantum number.
-The magnetic quantum number gives the number of orbitals and their orientation within the shell.
-The positive value of the spin quantum number implies an upward direction, that is the clockwise direction and the positive value of spin quantum number implies a downward direction, that is anticlockwise direction.