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  4. The magnetic moment of the ground state of an atom whose open sub shell is half filled with five electrons is

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Q. The magnetic moment of the ground state of an atom whose open sub shell is half filled with five electrons is

VITEEEVITEEE 2007

Solution:

The magnetic moment of the ground state of an atom is
$\mu=\sqrt{n(n+2)} \mu_{B}$
where $\mu_{B}$ is gyromagnetic moment. Here, open sub-shell is half-filled with 5 electrons.
i.e., $n=5$
$\therefore \mu=\sqrt{5(5+2)} \cdot \mu_{B}$
$=\mu_{B} \sqrt{35}$