Instead of principal quantum number (n), azimuthal quantum number `(l)` & magnetic quantum number (m), a set of new quantum number s, t & u was introduced with similar logic but different values as defined below
`s = 1, 2, 3,.......oo` all positive integral values.
`t = (s^(2) - 1^(2)), (s^(2) - 2^(2)), (s^(2) - 3^(2))`.........No negative value
`u = - ((t + 1))/(2) "to" + ((t + 1))/(2)` (including zero, if any) in integral steps.
Each orbital can have maximum four electrons.
`(s + t)` rule is defined, similar to `(n + l)` rule.
Number of electrons that can be accommodated in `s = 2` and `s = 3` shell.

Options

A. `14, 38
B. 28, 76
C. 8, 28
D. None of these

Answer

B

Explanation

`{:(s = 1,t = 0,u = - (1)/(2)","(1)/(2),),(s = 2,t = 0,u = - (1)/(2)","(1)/(2),),(,t = 3,u = - 2"," -1"," 0","+1","+2 ,),(s = 3,t = 0,u = - (1)/(2)","(1)/(2),),(,t = 5,u = -3"," -2"," -1"," 0"," +1"," +2"," +3,),(,t = 8,u = - (9)/(2) "," - (7)/(2)"," - (5)/(2)"," - (3)/(2)"," - (1)/(2)"," (1)/(2)"," (3)/(2)"," (5)/(2)"," (7)/(2)"," (9)/(2),):}`
According to `(s + t)` rule increasing order of energy
1s 2s 3s 4s 2f 5s
`{:((i),"Number of electron in " s = 2,7 xx 4 = 28,,),(,"Number of electron in " s = 3,19 xx 4 = 76,"Hence (B)",):}`
`{:((ii),"For " Z = 24,1s^(8) 2s^(8) 3s^(8) " i.e. number electrons (s) in " s = 2,t = 3 " " [2f^(@)] = 0,),(,"Hence" (C),,,):}`