Question

What would be the sum of all four quantum numbers associated with the unpaired electrons present in a nitrogen atom?
A. $10\dfrac{1}{2}$
B. $8\dfrac{1}{2}$
C. 7
D. 6

Answer 1

Hint: The atomic number of nitrogen is 7 means nitrogen contains 7 electrons. The electronic configuration of nitrogen is $1{{s}^{2}}2{{s}^{2}}2{{p}^{3}}$ . Means nitrogen contains 3 unpaired electrons in 2p orbital.

Complete step by step solution:
- In the question it is asked to find the sum of all four quantum numbers associated with the unpaired electrons present in a nitrogen atom.
- We are supposed to write the sum of all four quantum numbers associated with the unpaired electrons in 2p orbital.
- The principal quantum number (n) for 2p orbital is 2.
- The angular momentum quantum number (l) for 2p orbital is 1.
- The magnetic quantum number (m) for 2p orbital = -1, 0, +1
- The Spin quantum number (s) for unpaired electron is $\dfrac{1}{2}$

- We can write all the above quantum numbers individually as follows.
(1) n = 2, l = 1 , m = 1 and s = $\dfrac{1}{2}$ , the sum of these four quantum numbers = $2+1+1+\dfrac{1}{2}=4\dfrac{1}{2}$
(2) n = 2, l = 1 , m = 0 and s = $\dfrac{1}{2}$ , the sum of these four quantum numbers = $2+1+0+\dfrac{1}{2}=3\dfrac{1}{2}$
(3) n = 2, l = 1 , m = -1 and s = $\dfrac{1}{2}$ , the sum of these four quantum numbers = $2+1-1+\dfrac{1}{2}=2\dfrac{1}{2}$

- The sum of all the four quantum numbers associated with the unpaired electrons present in a nitrogen atom = $4\dfrac{1}{2}+3\dfrac{1}{2}+2\dfrac{1}{2}=10\dfrac{1}{2}$ .
- Therefore the sum of all four quantum numbers associated with the unpaired electrons present in a nitrogen atom is $10\dfrac{1}{2}$ .
So, the correct answer is “Option A”.

Note: To calculate the sum of the all four quantum numbers associated with the unpaired electrons present in a nitrogen atom we should know about the quantum numbers related to 2p orbital which contains unpaired electrons. We are not supposed to consider the paired electrons.