Question:

Consider the ground state of an atom (Z = 24). How many electrons are arranged with Azimuthal quantum number $ l = 1 $ and $ l = 2 $ respectively?

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The number of electrons in orbitals depends on the quantum numbers, with the $ p $-orbitals having a maximum of 6 electrons and $ d $-orbitals having a maximum of 10.

Updated On: Jan 14, 2026

12 and 4
16 and 4
12 and 5
12 and 5 and 6

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The Correct Option is C

Approach Solution - 1

The question asks about the distribution of electrons in the ground state for an atom with atomic number $ Z = 24 $. We need to find the number of electrons with azimuthal quantum numbers $ l = 1 $ and $ l = 2 $.

First, we determine the electron configuration for chromium ($ Z = 24 $) in its ground state:

Electron Configuration:

The electron configuration of chromium is $ 1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^6 \, 3d^5 \, 4s^1 $.

Now, we interpret the distribution of electrons for each principal energy level and their respective subshells by azimuthal quantum numbers:

The subshell $ s $ has $ l = 0 $.
The subshell $ p $ has $ l = 1 $.
The subshell $ d $ has $ l = 2 $.

Next, we identify how many electrons are in subshells corresponding to each azimuthal quantum number:

**Electrons with $ l = 1 $ (p subshells):**

$ 2p^6 $ — 6 electrons
$ 3p^6 $ — 6 electrons

Total electrons with $ l = 1 $: $ 6 + 6 = 12 $.

Electrons with $ l = 2 $ (d subshells):

$ 3d^5 $ — 5 electrons

Total electrons with $ l = 2 $: 5.

Therefore, the number of electrons with azimuthal quantum numbers $ l = 1 $ and $ l = 2 $ are 12 and 5, respectively.

Conclusion: The correct answer is 12 and 5.

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Approach Solution -2

The problem requires determining the number of electrons in the ground state of an atom with atomic number $ Z = 24 $ (chromium), that have azimuthal quantum numbers $ l = 1 $ and $ l = 2 $. Here is the step-by-step explanation:

The ground state electron configuration of an atom is determined by filling electrons in orbitals ranked by energy levels using the Aufbau principle. For chromium (atomic number $ Z = 24 $), the electron configuration is:

$ 1s^2 $ for $ n = 1, \, l = 0 $
$ 2s^2, \, 2p^6 $ for $ n = 2, \, l = 0, \, 1 $ (with $ 2p $ having 6 electrons, all with $ l = 1 $)
$ 3s^2, \, 3p^6 $ for $ n = 3, \, l = 0, \, 1 $ (with $ 3p $ having 6 electrons, all with $ l = 1 $)
$ 3d^5, \, 4s^1 $ for $ n = 3, \, 4 , \, l = 2, \, 0 $ (with $ 3d $ having 5 electrons, all with $ l = 2 $)

Identify the electrons with azimuthal quantum number $ l = 1 $:
- The electrons in $ 2p $ orbitals: 6 electrons for $ n = 2, \, l = 1 $.
- The electrons in $ 3p $ orbitals: 6 electrons for $ n = 3, \, l = 1 $.
Identify the electrons with azimuthal quantum number $ l = 2 $:
- The electrons in $ 3d $ orbitals: 5 electrons for $ n = 3, \, l = 2 $.
Hence, the number of electrons arranged with azimuthal quantum numbers $ l = 1 $ and $ l = 2 $ are respectively 12 and 5.

Therefore, the correct answer is: 12 and 5.

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