Chapter 11, Problem 31A

Interpretation Introduction

Interpretation: Pauli Exclusion Principle and number of electrons that can be accommodated in an orbital as per the principle is to be stated.

Concept introduction: Electronic configuration can be assigned to any elements in ground when they follow certain rules like Hund rule, Pauli Exclusion Principle and Aufbau rule. If atomic number of an element is $Z$ then $Z$ numbers of electrons are filled into the orbital which are arranged in increasing order of energy.

Answer to Problem 31A

No two electrons in an atom can have same group of four quantum numbers that is $n,l,m_l,m_s$ and this is Pauli Exclusion Principle. Maximum number of electron that can be contained in an orbital is 2 that too in opposite spin to cancel each other’s spin moment.

Explanation of Solution

No two electrons in an atom can have same group of four quantum numbers that is $n,l,m_l,m_s$ and this is Pauli Exclusion Principle. Maximum of electron that can be contained in an orbital is 2, so they must have opposite spin vale that is $m_s=+\frac{1}{2}\text{'}-\frac{1}{2}$ .

This is so if 2 electrons have same spin values that is $m_s=+\frac{1}{2},+\frac{1}{2}$ , then Pauli Exclusion Principle is violated and such atom doesn’t exist.

Conclusion

No two electrons in an atom can have same group of four quantum numbers that is $n,l,m_l,m_s$ and this is Pauli Exclusion Principle. Maximum number of electron that can be contained in an orbital is 2 that too in opposite spin to cancel each other’s spin moment.