Sum of all four quantum numbers associated with the unpaired electrons of nitrogen atom

To determine the sum of all four quantum numbers associated with the unpaired electrons of a nitrogen atom, we first need to understand the concept of quantum numbers and their significance in describing the electron configuration.

Quantum Numbers
Quantum numbers are mathematical values that describe various properties of an electron in an atom. They provide information about the energy, orbital shape, orientation, and spin of an electron. There are four quantum numbers: principal quantum number (n), azimuthal quantum number (l), magnetic quantum number (m), and spin quantum number (s).

The Principal Quantum Number (n)
The principal quantum number (n) represents the energy level or shell in which an electron resides. It can have integral values starting from 1, 2, 3, and so on. The larger the value of n, the higher the energy level and the farther the electron is from the nucleus.

The Azimuthal Quantum Number (l)
The azimuthal quantum number (l) determines the shape of the orbital in which an electron is present. It depends on the value of n and can range from 0 to (n-1). The different values of l correspond to different orbital shapes. For example, l=0 corresponds to an s orbital, l=1 corresponds to a p orbital, l=2 corresponds to a d orbital, and so on.

The Magnetic Quantum Number (m)
The magnetic quantum number (m) specifies the orientation of the orbital in space. It can range from -l to +l, including zero. For example, if l=1 (p orbital), m can have values of -1, 0, and 1, representing the three different orientations of the p orbital along the x, y, and z axes.

The Spin Quantum Number (s)
The spin quantum number (s) describes the spin state of an electron within an orbital. It can have two possible values: +1/2 (spin-up) or -1/2 (spin-down).

Unpaired Electrons in Nitrogen Atom
The electron configuration of a nitrogen atom is 1s2 2s2 2p3. It has a total of five electrons, and three of them occupy the 2p orbital. As per Hund's rule, electrons will first occupy separate orbitals with the same spin before pairing up.

Sum of Quantum Numbers for the Unpaired Electrons in Nitrogen Atom
For the three unpaired electrons in the 2p orbital of a nitrogen atom, we can determine the sum of the quantum numbers as follows:

1. Principal Quantum Number (n): The 2p orbitals belong to the n=2 energy level.

2. Azimuthal Quantum Number (l): The p orbitals have l=1.

3. Magnetic Quantum Number (m): The three p orbitals have magnetic quantum numbers m=-1, 0, and 1, representing the three different orientations.

4. Spin Quantum Number (s): The unpaired electrons can have either +1/2 or -1/2 values for the spin quantum number.

To find the sum of the quantum numbers, we add up the values of n, l, m, and s for each unpaired electron. Let's consider the