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 atomic number \( Z = 24 \), indicating 24 electrons. Its electron configuration is: \[ \text{Cr: } [Ar] 3d^5 4s^1 \] Now, consider the azimuthal quantum number \( l \) and its associated orbitals: - When \( l = 1 \), the orbitals are \( p \)-orbitals, which can hold a total of 6 electrons. In chromium, the \( 3p \) and \( 4p \) orbitals contribute to this, each capable of holding 6 electrons. Therefore, for \( l = 1 \), there are 6 electrons. - When \( l = 2 \), the orbitals are \( d \)-orbitals, with a maximum capacity of 10 electrons. In chromium's configuration \( 3d^5 \), the \( 3d \) orbitals contain 5 electrons. Combining these, for \( l = 1 \), there are 6 electrons (from \( p \)-orbitals), and for \( l = 2 \), there are 10 electrons (from \( d \)-orbitals). The total number of electrons for these \( l \) values is: \[ 6 \text{ (from \( p \)-orbitals)} + 10 \text{ (from \( d \)-orbitals)} = 12 \text{ electrons}. \] Thus, chromium has a total of 12 electrons with \( l = 1 \) and \( l = 2 \). Consequently, the correct answer is (2) 12.