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JEE MainChemistryStructure of Atom

In a particular principal shell of an atom, the maximum number of electrons that can simultaneously have the magnetic quantum number m_l = +1 and the spin quantum number m_s = -1/2 is 4 . The principal quantum number n of this shell is ______

Correct answer

5

Step-by-step solution

The condition m_s = -1/2 restricts the count to exactly 1 electron per valid orbital. Since there are 4 such electrons, there must be exactly 4 orbitals with m_l = +1 in the n^ th shell. The magnetic quantum number m_l = +1 is only possible for subshells with azimuthal quantum number l 1 . In the n^ th shell, l ranges from 0 to n-1 . The number of subshells with l 1 is (n-1) . Each of these subshells contributes exactly one orbital with m_l = +1 . Equating the number of such subshells to the number of orbitals give

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