Question

Total number of electrons in chromium (Z = 24) for which the value of azimuthal quantum number (l) is 1 and 2.

• A. 10
• B. 12
• C. 14
• D. 16

Hint:

The azimuthal quantum number \( l \) determines the shape of the orbital. For \( l = 1 \), the orbital is a \( p \)-orbital, which can hold 6 electrons, and for \( l = 2 \), the orbital is a \( d \)-orbital, which can hold 10 electrons.

Answer 1

The Correct Option is B

Chromium (Cr) has an atomic number \( Z = 24 \), meaning it has 24 electrons. The electron configuration of chromium is: \[ \text{Cr: } [Ar] 3d^5 4s^1 \] Now, let’s examine the azimuthal quantum number \( l \) and its corresponding orbitals: - For \( l = 1 \), the electron orbital corresponds to the \( p \)-orbitals. These can accommodate 6 electrons in total, with the electron configuration including the \( 3p \) orbitals and the \( 4p \) orbitals. In chromium, the \( 3p \) and \( 4p \) orbitals can each hold 6 electrons. So, for \( l = 1 \), there are 6 electrons. - For \( l = 2 \), the electron orbital corresponds to the \( d \)-orbitals. These can hold a maximum of 10 electrons. In the case of chromium, the \( 3d \) orbitals can accommodate 5 electrons (as seen in the configuration \( 3d^5 \)). Thus, for \( l = 1 \), there are 6 electrons (from \( p \)-orbitals) and for \( l = 2 \), there are 10 electrons (from \( d \)-orbitals). Therefore, the total number of electrons corresponding to these values of \( l \) is: \[ 6 \text{ (from \( p \)-orbitals)} + 10 \text{ (from \( d \)-orbitals)} = 12 \text{ electrons}. \] Thus, the total number of electrons in chromium for which \( l = 1 \) and \( l = 2 \) is 12. Therefore, the correct answer is (2) 12.