Chemistry Q51 – JEE-MAIN 2025

Home Chemistry Structure of AtomQuestion #623

Correct statements for an element with atomic number 9 are A. There can be 5 electrons for which

m_{s} = + \frac{1}{2}

and 4 electrons for which

m_{s} = - \frac{1}{2}

. B. There is only one electron in

p_{z}

orbital. C. The last electron goes to orbital with

n = 2

and

l = 1

. D. The sum of angular nodes of all the atomic orbitals is 1. Choose the correct answer from the options given below:

Clue 1 of 3: Electron Configuration and Quantum Numbers

Determine the electron configuration for the given atomic number and recall the definitions of quantum numbers and nodes.

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Ninja Strategy•Eliminate based on D and B's ambiguity

Statement D is definitively incorrect, eliminating options 2 and 4. Statement B is problematic due to the arbitrary assignment of the single electron to a specific $p_{z}$ orbital, making A and C the most robustly correct statements.

🧠 Full Solution Path

Step 1: Determine Electron Configuration and Evaluate Spin Distribution (Statement A)✦ Active

The element with atomic number 9 is Fluorine (F). Its electron configuration is $1 s^{2} 2 s^{2} 2 p^{5}$ . Total electrons = 9. According to the Pauli exclusion principle, for an odd number of electrons, there will be $(N + 1) / 2$ electrons with one spin ( $+ 1 / 2$ ) and $(N - 1) / 2$ electrons with the other spin ( $- 1 / 2$ ). Thus, the number of electrons with $m_{s} = + 1 / 2 = (9 + 1) / 2 = 5$ , and the number of electrons with $m_{s} = - 1 / 2 = (9 - 1) / 2 = 4$ . Statement A is correct.

Step 2: Evaluate Orbital Filling and Quantum Numbers (Statements B and C)○ Expand

For $2 p^{5}$ , the five electrons are distributed among the three degenerate $2 p$ orbitals ( $2 p_{x}, 2 p_{y}, 2 p_{z}$ ) according to Hund's rule. This results in two orbitals having two electrons and one orbital having a single electron (e.g., $2 p_{x}^{2} 2 p_{y}^{2} 2 p_{z}^{1}$ ). Statement B claims "There is only one electron in $p_{z}$ orbital." While one of the $p$ orbitals will have one electron, specifying $p_{z}$ is arbitrary and not universally true without defining the orientation, making statement B strictly incorrect. The last electron (9th electron) enters the $2 p$ subshell. For a $2 p$ orbital, the principal quantum number $n = 2$ and the azimuthal quantum number $l = 1$ . Statement C is correct.

Step 3: Calculate Sum of Angular Nodes (Statement D)○ Expand

The number of angular nodes for an orbital is given by its azimuthal quantum number $l$ . The occupied orbitals are $1 s, 2 s, 2 p_{x}, 2 p_{y}, 2 p_{z}$ . The $l$ values are: $1 s (l = 0)$ , $2 s (l = 0)$ , $2 p_{x} (l = 1)$ , $2 p_{y} (l = 1)$ , $2 p_{z} (l = 1)$ . The sum of angular nodes of all the atomic orbitals = $0 + 0 + 1 + 1 + 1 = 3$ . Therefore, statement D is incorrect. Based on the analysis, only statements A and C are correct.

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Chemistry Question 51 – JEE-MAIN 2025

Clue 1 of 3: Electron Configuration and Quantum Numbers

🧠 Full Solution Path