Question

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Class 10 advance chemistry

Answer 1

The four different Quantum Numbers are:

1) Principal Quantum Number (n)


This denotes the shell in which the electron is. That is, it denotes the orbit.


2) Azimuthal Quantum Number (l)


It denotes the subshell. The value of $l$ can range from 0 to (n-1). It represents the shape of the subshell.


3) Magnetic Quantum Number (m)


It denotes the orbital. Its value can range from $-l$ to $+l$. It represents the orientation of orbital in space.


4) Spin Quantum Number (s)


It denotes the Spin of an electron present in an orbital. It can take values of $+\frac{1}{2}$ or $-\frac{1}{2}$


Each electron has a unique combination of these four quantum numbers.


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Coming to the question.


We are given the $_{15}P$ atom.


There are 5 electrons: A, B, X, Y, and Z. 

A and B are 3s electrons. And also, B has a spin of $+{}^1{\mskip -5mu/\mskip -3mu}_2$.



Pauli's Exclusion Principle states that no two electrons in an atom can have the same values of all four quantum numbers.

So, automatically, A has a spin of $-{}^1{\mskip -5mu/\mskip -3mu}_2$

So we have the following config for A and B:


$\boxed{\begin{array}{cc}A & B \\ \\ \begin{array}{ccc} n&=&3 \\ l&=&0 \\ m&=&0 \\ s&=&-{}^1{\mskip -5mu/\mskip -3mu}_2 \end{array} & \begin{array}{ccc} n&=&3 \\ l&=&0 \\ m&=&0 \\ s&=&+{}^1{\mskip -5mu/\mskip -3mu}_2 \end{array} \end{array}}$


We see that A and B only differ in the Spin Quantum Number. Their other three quantum numbers are the same.

So, our answer contains the pair A and B.


Coming to X, Y and Z.
All of them are 3p electrons. 


Also, Z has a spin of $-{}^1{\mskip -5mu/\mskip -3mu}_2$. 


The 3p subshell has three orbitals: $p_x$, $p_y$ and $p_z$. 

Also, Hund's Rule of Maximum Multiplicity states that all the orbitals of a subshell must be filled singly with same-spin electrons. 

So, we know that X, Y, Z all belong to different orbitals but have the same spin.


The configuration of X, Y and Z are:

$\boxed{\begin{array}{ccc} X & Y & Z \\ \\ \begin{array}{ccc} n&=&3 \\ l&=&1 \\ m&=&0 \\ s&=&+{}^1{\mskip -5mu/\mskip -3mu}_2 \end{array} & \begin{array}{ccc} n&=&3 \\ l&=&1 \\ m&=&1 \\ s&=&+{}^1{\mskip -5mu/\mskip -3mu}_2 \end{array} & \begin{array}{ccc} n&=&3 \\ l&=&1 \\ m&=&2\\ s&=&+{}^1{\mskip -5mu/\mskip -3mu}_2 \end{array} \end{array}}$


X, Y, and Z only differ in the Magnetic Quantum Number. So we see that they also have three quantum numbers in common.

So, our answer must also contain X, Y, and Z as a group.


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Thus, Finally, The Answer is Option (2) AB, XYZ