Answer
See the explanation
Work Step by Step
a. In this universe, the periodic table will have a different structure due to the different quantum number rules. The first four periods of the periodic table will look like this:
1st period: \( p=1 \), \( q=1 \), \( r=0 \), \( s=+\frac{1}{2} \) or \( -\frac{1}{2} \) (2 elements)
2nd period: \( p=2 \), \( q=1 \), \( r=0 \), \( s=+\frac{1}{2} \) or \( -\frac{1}{2} \) (2 elements)
3rd period:
\( p=3 \), \( q=1 \), \( r=0 \), \( s=+\frac{1}{2} \) or \( -\frac{1}{2} \) (2 elements)
\( p=3 \), \( q=3 \), \( r=-2 \), \( s=+\frac{1}{2} \) or \( -\frac{1}{2} \) (2 elements)
\( p=3 \), \( q=3 \), \( r=0 \), \( s=+\frac{1}{2} \) or \( -\frac{1}{2} \) (2 elements)
\( p=3 \), \( q=3 \), \( r=+2 \), \( s=+\frac{1}{2} \) or \( -\frac{1}{2} \) (2 elements)
4th period: \( p=4 \); $q$ and $r$ have the same values, so there is a total of 8 elements
b. The atomic numbers of the first four elements expected to be least reactive would be determined by the quantum numbers. In this case, the first four elements with the least reactivity would be the elements with filled shells: 2, 4, 12, 20.
c. Ionic compounds with the given formulas can be constructed using elements in the first four rows based on their quantum numbers.
$X^+Y^-,X^{2+}Y^{2-},X^{3+}Y^{3-}$
Examples:
$X^+$ can be one of the elements 1, 3, 5,13, while $Y^-$ can be 11 or 19.
$X^{2+}$ can be one of the elements 6,14, while $Y^{2-}$ can be 10 or 18.
$X^{3+}$ can be one of the elements 7,15, while $Y^{3-}$ can be 9 or 17.
d. For \( p=4, q=3 \), the number of electrons is \(2+2+2=6 \) electrons.
e. For \( p=3, q=0, r=0 \) is not allowed as $q$ must be odd..
f. For \( p=6 \), the number of electrons can be calculated as follows \(2+6+10 = 18 \) electrons.
