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?

• A. 12 and 4
• B. 16 and 4
• C. 12 and 5
• D. 12 and 5 and 6

Hint:

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.

Answer 1

The Correct Option is C

The question concerns the electron distribution in the ground state of an atom with atomic number \( Z = 24 \). Specifically, it requires determining the number of electrons with azimuthal quantum numbers \( l = 1 \) and \( l = 2 \).

The electron configuration for chromium (\( Z = 24 \)) in its ground state is established first.

Electron Configuration:

The ground-state electron configuration for chromium is \( 1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^6 \, 3d^5 \, 4s^1 \).

The distribution of electrons across principal energy levels and their corresponding subshells, categorized by azimuthal quantum numbers, is then interpreted:

• Subshells with \( l = 0 \) correspond to the \( s \) type.
• Subshells with \( l = 1 \) correspond to the \( p \) type.
• Subshells with \( l = 2 \) correspond to the \( d \) type.

The number of electrons within subshells associated with each azimuthal quantum number is subsequently identified:

Electrons with \( l = 1 \) (p subshells):

• From \( 2p^6 \): 6 electrons
• From \( 3p^6 \): 6 electrons

The total count of electrons with \( l = 1 \) is \( 6 + 6 = 12 \).

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

• From \( 3d^5 \): 5 electrons

The total count of electrons with \( l = 2 \) is 5.

Consequently, the number of electrons with azimuthal quantum numbers \( l = 1 \) and \( l = 2 \) are 12 and 5, respectively.

Conclusion: The values are 12 and 5.