1. n= 2,1= 2 2 n= 4,1= 1 3. I=3 , ml= +3 Find the maximum number of electrons in a given atom that can have the following quantum numbers. 1. n=3, l=2 2 n=4, 1 =1 3. I=2, ml=+3

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**Quantum Numbers: Understanding Possibilities and Electron Configurations**

**Question 1: Determining Impossible Quantum Numbers**

Which of the following sets of quantum numbers is/are impossible?
1. \( n = 2, \, l = 2 \)
2. \( n = 4, \, l = 1 \)
3. \( l = 3, \, m_l = +3 \)

**Question 2: Maximum Electrons with Given Quantum Numbers**

Find the maximum number of electrons in a given atom that can have the following quantum numbers.
1. \( n = 3, \, l = 2 \)
2. \( n = 4, \, l = 1 \)
3. \( l = 2, \, m_l = +3 \)

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Quantum numbers are crucial for understanding the arrangement of electrons in an atom. Each electron in an atom can be identified with a set of four quantum numbers: the principal quantum number (\( n \)), the azimuthal quantum number (\( l \)), the magnetic quantum number (\( m_l \)), and the spin quantum number (\( m_s \)). These numbers help specify the electron's energy level, shape of the orbital, orientation of the orbital, and spin direction, respectively.
Transcribed Image Text:**Quantum Numbers: Understanding Possibilities and Electron Configurations** **Question 1: Determining Impossible Quantum Numbers** Which of the following sets of quantum numbers is/are impossible? 1. \( n = 2, \, l = 2 \) 2. \( n = 4, \, l = 1 \) 3. \( l = 3, \, m_l = +3 \) **Question 2: Maximum Electrons with Given Quantum Numbers** Find the maximum number of electrons in a given atom that can have the following quantum numbers. 1. \( n = 3, \, l = 2 \) 2. \( n = 4, \, l = 1 \) 3. \( l = 2, \, m_l = +3 \) --- Quantum numbers are crucial for understanding the arrangement of electrons in an atom. Each electron in an atom can be identified with a set of four quantum numbers: the principal quantum number (\( n \)), the azimuthal quantum number (\( l \)), the magnetic quantum number (\( m_l \)), and the spin quantum number (\( m_s \)). These numbers help specify the electron's energy level, shape of the orbital, orientation of the orbital, and spin direction, respectively.
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