Question:

If \(n,l,m\) and \(s\) represent the symbols of quantum numbers, the impossible quantum number set for the electron in terms of \(n,l,m\) and \(s\) respectively is

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For a given \(l\), magnetic quantum number \(m\) can take values from \(-l\) to \(+l\). If \(l=0\), then only \(m=0\) is possible.
  • \(2,0,-1,+\frac{1}{2}\)
  • \(3,0,0,-\frac{1}{2}\)
  • \(4,1,+1,+\frac{1}{2}\)
  • \(3,2,-1,-\frac{1}{2}\)
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The Correct Option is A

Solution and Explanation

For quantum numbers, the rules are: Principal quantum number: \[ n=1,2,3,\ldots \] Azimuthal quantum number: \[ l=0,1,2,\ldots,n-1. \] Magnetic quantum number: \[ m=-l,\ldots,0,\ldots,+l. \] Spin quantum number: \[ s=+\frac{1}{2}\quad \text{or}\quad -\frac{1}{2}. \] Now check option (A): \[ n=2,\quad l=0,\quad m=-1,\quad s=+\frac{1}{2}. \] If: \[ l=0, \] then magnetic quantum number can only be: \[ m=0. \] But option (A) gives: \[ m=-1. \] This is not allowed. Therefore, option (A) is impossible.
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