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(C) For a given principal quantum number $n$,the possible values of the azimuthal quantum number $l$ range from $0$ to $n-1$.For $n = 5$,$l$ can be $0

Vedclass · Accepted Answer

$6$

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(C) For a given principal quantum number $n$,the possible values of the azimuthal quantum number $l$ range from $0$ to $n-1$.For $n = 5$,$l$ can be $0, 1, 2, 3, 4$.The magnetic quantum number $m_l$ depends on $l$ and ranges from $-l$ to $+l$.We need to find the orbitals where $m_l = +2$ is possible:- If $l = 0$ ($s$-orbital): $m_l = 0$ (not possible)- If $l = 1$ ($p$-orbital): $m_l = -1, 0, +1$ (not possible)- If $l = 2$ ($d$-orbital): $m_l = -2, -1, 0, +1, +2$ (possible)- If $l = 3$ ($f$-orbital): $m_l = -3, -2, -1, 0, +1, +2, +3$ (possible)- If $l = 4$ ($g$-orbital): $m_l = -4, -3, -2, -1, 0, +1, +2, +3, +4$ (possible)Thus,for $n = 5$,the orbitals with $m_l = +2$ are $5d, 5f,$ and $5g$.Each orbital can hold a maximum of $2$ electrons.Total electrons = $3 	ext{ orbitals} 	imes 2 	ext{ electrons/orbital} = 6 	ext{ electrons}$.

What is the maximum number of electrons that can have the quantum numbers $n = 5$ and $m_l = +2$?

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