Question

In $\mathrm{Cr}$, determine the minimum and maximum number of electrons for which the magnetic quantum number $\mathrm{m}=+1$ and the spin quantum number $s=-\frac{1}{2}$.

(A) 0,1
(B) 1,2
(C) 4,6
(D) 2,3

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Answer

The correct answer is: D

In the chromium atom ($\mathrm{Cr}$), we need to determine the minimum and maximum number of electrons for which the magnetic quantum number $m=+1$ and the spin quantum number $s=-\frac{1}{2}$.

  1. For the 2p and 3p orbitals:

    • Each of these orbitals has a total of 6 electrons.
    • Among these electrons, one can have $m=+1$ and $s=-\frac{1}{2}$.
  2. For the 3d sub-shell:

    • In the 3d sub-shell, the orbital with $m=+1$ can have electrons with spin quantum numbers $s = -\frac{1}{2}$ or $s = +\frac{1}{2}$.

Thus, the minimum possible value is 2, and the maximum possible value is 3.

Hence, the minimum and maximum possible numbers are $\textbf{2 and 3}$ respectively.

Final Answer: D


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