Quantum Numbers

Quantum numbers is a scientific set of numbers used to define the energy and position of an electron in an atom. This also represents the trajectory and movement of each electron. The numbers of all electrons in a single atom must and will produce complying solutions for Schrodinger’s Wave Equation. A quantum number can only be an integer value or half of any integer value. Each electron in an atom has four types of numbers defining their set of quantum values:

• Principal Quantum Number (n)
• Azimuthal or Angular Momentum Quantum Number (l)
• Magnetic Quantum Number (m or ml)
• Spin Quantum Number (s or ms)

Let us learn the definitions of each number and its distinctions from one another:

Principal Quantum Number:

• This number is related to the shell of atoms. It is represented by ‘n’. This quantum number refers to the probable distance between the nucleus and the electron present in the atom

• The value of this number can either be equal to or more than 1. It must always be a positive integer. When this value of an electron is 1, it means the electron is in the first or principal electron shell of an atom. This is the lowest energy state of an electron

• From the above point, it is evident why the value cannot be lower than 1. This is because the principal shell of an atom is the lowest energy state of an electron

• However, a change in this value can occur. If energy is provided or deducted from an electron, it can cause a shift in its energy level. Providing energy excites an electron. This causes them to jump from a lower energy state to a higher one. This phenomenon is known as absorption. A decrease in the energy level shifts them to a lower energy state. This phenomenon of electron releasing energy is known as emission

• This number can be used to denote the size of an atom. Larger the value, the greater is the atomic radius and vice-versa

Azimuthal Quantum Number (Orbital Angular Momentum Quantum Number):

• This value is used to represent the shape of the orbital the electron is present in. It is denoted by ‘l’. This number tells us the number of angular nodes in the said orbital. This value is a numeric value that indicates the subshells represented by an alphabetic character. This value is dependent on the principal quantum number too
• This value of the azimuthal quantum number denotes the s, p, d, and f subshells. These are varying in shape. This value can never be a negative or half of an integer. This number can range from 0 to (n-1)

• One can see how from the principal quantum number we can derive possible values of the azimuthal. For more clarity, let n = 4. Hence, the values can be {0, 1, 2, 3}. When l = 0, the said electron is in the ‘s’ subshell. When l = 1 then it is being referred to p, l = 2 then d subshell is referred, and for l = 3, subshell f is indicated

• As mentioned before, this number also represents the number of angular nodes. Hence, from this number, the number of angular nodes in each subshell can be derived

Magnetic Quantum Number:

• This value determines the orbitals and their orientations in the subshells. It is denoted by “ml” for short. This value is dependent on the value of the azimuthal quantum number, meaning indirectly related to the principal quantum number as well

• The magnetic quantum number is dependent on the Orbital Angular Momentum quantum number. The possible values of ml range from negative to positive azimuthal quantum numbers. The number of values in the set of possible ml is used to determine the number of orbitals in the subshell

• However, to shorten time one can use a quick and easy formula to find the number of orbitals in the subshell. This formula is: (2*l + 1). To prove the formula’s validity, let us take an example

Let the azimuthal quantum value be 2 (meaning the ‘d’ subshell). The number of possibilities of the magnetic quantum number is {-2, -1, 0, 1, 2}. Since there are 5 possible values, we can determine there are 5 orbitals in the subshell. Now, let us place the predefined quantum value, that is l, in the formula. We get, (2*2+1) = (4+1) = 5. Hence, there are 5 orbitals that we had derived previously.

Electron Spin Quantum Number:

• Unlike the aforementioned types, this quantum number is independent of the others. This value is used to determine the direction the electron is spinning in. In short, this value is denoted by ms. These are also denoted using symbols such as the up and down arrows

• The value of this number can only be – ½ and +½. These are used to determine their ability to induce a magnetic field surrounding them

• When an electron has a positive half-integer value it is referred to as ‘spin up’ as the electron spin is upwards. When an electron has a negative half-integer value for ms , it implies a downward spin and is said to have been ‘spin down’. These are pictorially depicted as ↑ and ↓ respectively

We know that no two electrons can share exactly identical sets of quantum number values. This is because each orbital can only contain two electrons of the opposite spins. These four numbers combined can narrow down the possible locations of an electron in an atom