Question:
The d-electronic configuration of $\left[ CoCl _4\right]^{2-}$ in tetrahedral crystal field is $e ^{ m } t _2 ^n$ Sum of "$m$" and "number of unpaired electrons" is
The d-electronic configuration of $\left[ CoCl _4\right]^{2-}$ in tetrahedral crystal field is $e ^{ m } t _2 ^n$ Sum of "$m$" and "number of unpaired electrons" is
Updated On: Mar 19, 2025
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Correct Answer: 7
Solution and Explanation
Given:
- Oxidation state of Co: \( \text{Co}^{2+} \) (\( \text{Co} = 3d^7 4s^0 \)).
- Geometry: Tetrahedral crystal field, where weak field ligands (\( \text{Cl}^- \)) cause small splitting.
- Electronic configuration in tetrahedral field: \( t_2^4 e^3 \).
Step 1: Determine ‘m’. - \( t_2 \)-orbital contains 4 electrons (\( m = 4 \)).
Step 2: Determine unpaired electrons. - In \( t_2^4 e^3 \), the total number of unpaired electrons is 3.
Final Calculation: Sum of \( m + \text{(number of unpaired electrons)} = 4 + 3 = 7 \).
Step 1: Determine ‘m’. - \( t_2 \)-orbital contains 4 electrons (\( m = 4 \)).
Step 2: Determine unpaired electrons. - In \( t_2^4 e^3 \), the total number of unpaired electrons is 3.
Final Calculation: Sum of \( m + \text{(number of unpaired electrons)} = 4 + 3 = 7 \).
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Concepts Used:
Subshell Electronic Configuration
Electron Configuration is referred to as the distribution of electrons in an atom's orbitals. An electron in an atom is defined by a set of four quantum numbers (n), the most important of which defines the main energy level known as a shell. The filling of electrons into different subshells, also known as orbitals (s, p, d, f) in an atom. The position of an element in the periodic table is determined by the quantum numbers of the last orbital filled.
Subshells:
- The azimuthal quantum number (denoted by 'l') determines the subshells into which electrons are distributed.
- The value of this quantum number is determined by the value of the principal quantum number, n. As a result, when n equals 4, four different subshells are possible.
- When n = 4, The s, p, d, and f subshells correspond to l=0, l=1, l=2, and l=3 values, respectively.
- The formula 2*(2l + 1) gives the maximum number of electrons that a subshell can accommodate.
- As a result, the s, p, d, and f subshells can each hold a maximum of 2, 6, 10, and 14 electrons.