From the following data, the number of electrons belongs to $S = 2 a n d t = 3$ for an element with atomic number $Z = 24$ is______
Instead of principal quantum number (n), Azimuthal quantum number $(l)$ and magnetic quantum number (m), a set of new quantum number S, t and u were introduced with similar logic but different values as defined below:
$S=1,2,3, ........... \infty (all +ve integral values) t= (S^{2} {-1}^{2}), (S^{2} {-2}^{2}), (S^{2} {-3}^{2}) ........ (non negative values)$
$U= - (\frac{t + 1}{2}) to + (\frac{t + 1}{2})$ (Including zero, if $' t'$ has odd value) in integral steps.
Each orbital can have maximum four electrons. $(S + t)$ rule is defined similar to $(n + l)$ rule.

Question

From the following data, the number of electrons belongs to $S = 2 a n d t = 3$ for an element with atomic number $Z = 24$ is______
Instead of principal quantum number (n), Azimuthal quantum number $(l)$ and magnetic quantum number (m), a set of new quantum number S, t and u were introduced with similar logic but different values as defined below:
$S=1,2,3, ........... \infty (all +ve integral values) t= (S^{2} {-1}^{2}), (S^{2} {-2}^{2}), (S^{2} {-3}^{2}) ........ (non negative values)$
$U= - (\frac{t + 1}{2}) to + (\frac{t + 1}{2})$ (Including zero, if $' t'$ has odd value) in integral steps.
Each orbital can have maximum four electrons. $(S + t)$ rule is defined similar to $(n + l)$ rule.

Infinity Learn · Accepted Answer

Total electronsS=1t=0u=12,122×4=8S=2 t=0u=−12,+12u=−3,−2,−1,0,+1,+2,+32×4=8S=3t=0 t=5 t=8 u=−12,+12 u=−5,−4,−3,−1,0,+1,+2,+3,+4,+5 u=−8,−7...............+7,+8 7×4=2811×4=44 16×4=64(S+t) rule (energies)1+0=0(8e−) 2+0=2(8e−) 3+0=3(8e−) 2+3=5(28e−)

			Total electrons
$S = 1$	$t = 0$	$u = \frac{1}{2}, \frac{1}{2}$	$2 \times 4 = 8$
$S = 2$	$t = 0$	$u = \frac{- 1}{2}, \frac{+ 1}{2}$ $u = - 3, - 2, - 1, 0, + 1, + 2, + 3$	$2 \times 4 = 8$
$S = 3$	$t = 0 t = 5 t = 8$	$u = \frac{- 1}{2}, \frac{+ 1}{2} u = - 5, - 4, - 3, - 1, 0, + 1, + 2, + 3, + 4, + 5 u = - 8, - 7............... + 7, + 8$	$7 \times 4 = 28$ $11 \times 4 = 44 16 \times 4 = 64$

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