Chemistry Q53 – JEE-MAIN 2026

Home Chemistry Structure of AtomQuestion #601

Which of the following is correct set of 4 quantum numbers of

19^{t h}

electron in Chromium (Atomic number = 24) in accordance with Aufbau principle?

Clue 1 of 3: Aufbau Principle

Determine the order of filling atomic orbitals based on increasing energy.

🧠 Full Solution Path

Step 1: Determine the electron configuration up to the

19^{t h}

electron✦ Active

Following the Aufbau principle, electrons fill atomic orbitals in increasing order of energy. The sequence is $1 s, 2 s, 2 p, 3 s, 3 p, 4 s, 3 d, . . .$ . Let's fill the electrons for Chromium (Z=24) up to the $19^{t h}$ electron:

1 s^{2} (2 electrons)

2 s^{2} (4 electrons)

2 p^{6} (10 electrons)

3 s^{2} (12 electrons)

3 p^{6} (18 electrons)

After filling $3 p^{6}$ , we have accounted for 18 electrons. The $19^{t h}$ electron will enter the next available orbital according to the Aufbau principle, which is the $4 s$ orbital.

Step 2: Identify the quantum numbers for the

19^{t h}

electron○ Expand

Since the $19^{t h}$ electron is in the $4 s$ orbital, we can determine its quantum numbers:

- Principal quantum number ( $n$ ): For the $4 s$ orbital, $n = 4$ .

- Azimuthal quantum number ( $l$ ): For an $s$ orbital, $l = 0$ .

- Magnetic quantum number ( $m_{l}$ ): For $l = 0$ , the only possible value for $m_{l}$ is $0$ .

- Spin quantum number ( $m_{s}$ ): Conventionally, the first electron entering an orbital is assigned $m_{s} = + \frac{1}{2}$ .

Thus, the set of quantum numbers for the $19^{t h}$ electron is $n = 4, l = 0, m = 0, s = + \frac{1}{2}$ .

💡 Teacher's Secret Hint

Remember the rules for possible values of $l$ (from $0$ to $n - 1$ ) and $m_{l}$ (from $- l$ to $+ l$ ). The spin quantum number can be either $+ 1 / 2$ or $- 1 / 2$ .

Step 3: Match with the given options○ Expand

Comparing the derived set of quantum numbers ( $n = 4, l = 0, m = 0, s = + \frac{1}{2}$ ) with the provided options:

- Option 1: $n = 3, l = 2, m = + 2, s = + \frac{1}{2}$ (Incorrect, this is a $3 d$ orbital)

- Option 2: $n = 3, l = 2, m = - 2, s = + \frac{1}{2}$ (Incorrect, this is a $3 d$ orbital)

- Option 3: $n = 4, l = 1, m = 0, s = + \frac{1}{2}$ (Incorrect, this is a $4 p$ orbital)

- Option 4: $n = 4, l = 0, m = 0, s = + \frac{1}{2}$ (Correct, this is a $4 s$ orbital)

Therefore, option 4 is the correct set of quantum numbers.

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Chemistry Question 53 – JEE-MAIN 2026

Clue 1 of 3: Aufbau Principle

🧠 Full Solution Path