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The quantum number of four electrons are...

The quantum number of four electrons are given below:
I. `n=4,l=2,m_l=-2,m_s=-1/2` II. `n=3,l=2,m_l=1,m_s=+1/2`
`III. n = 4 , l =1 ,m _l=0 ,m_s=+1/2`
IV. `n=3,l=1,m_l=1,m_s=-1/2`
The correct order of their increasing energies will be

A

`IgtIIgtIIIgtIV`

B

`IVgtIIIgtIIgtI`

C

`IVgtIIgtIIIgtI`

D

`IgtIIIgtIIgtIV`

Text Solution

AI Generated Solution

The correct Answer is:
To determine the correct order of increasing energies for the given quantum numbers of four electrons, we will apply the n + l rule. This rule states that the energy of an electron in an atom is primarily determined by the sum of its principal quantum number (n) and its azimuthal quantum number (l). The lower the value of n + l, the lower the energy of the electron. ### Step-by-Step Solution: 1. **Identify the quantum numbers for each electron:** - Electron I: \( n = 4, l = 2 \) → \( n + l = 4 + 2 = 6 \) - Electron II: \( n = 3, l = 2 \) → \( n + l = 3 + 2 = 5 \) - Electron III: \( n = 4, l = 1 \) → \( n + l = 4 + 1 = 5 \) - Electron IV: \( n = 3, l = 1 \) → \( n + l = 3 + 1 = 4 \) 2. **List the values of n + l for each electron:** - Electron I: \( n + l = 6 \) - Electron II: \( n + l = 5 \) - Electron III: \( n + l = 5 \) - Electron IV: \( n + l = 4 \) 3. **Order the electrons based on their n + l values:** - The lowest value of \( n + l \) corresponds to the lowest energy: - Electron IV: \( n + l = 4 \) (3p) - Electron II: \( n + l = 5 \) (3d) - Electron III: \( n + l = 5 \) (4p) - Electron I: \( n + l = 6 \) (4d) 4. **Establish the correct order of increasing energy:** - From lowest to highest energy: - Electron IV (3p) < Electron II (3d) < Electron III (4p) < Electron I (4d) ### Final Order of Increasing Energies: - Electron IV < Electron II < Electron III < Electron I
To determine the correct order of increasing energies for the given quantum numbers of four electrons, we will apply the n + l rule. This rule states that the energy of an electron in an atom is primarily determined by the sum of its principal quantum number (n) and its azimuthal quantum number (l). The lower the value of n + l, the lower the energy of the electron. ### Step-by-Step Solution: 1. **Identify the quantum numbers for each electron:** - Electron I: \( n = 4, l = 2 \) → \( n + l = 4 + 2 = 6 \) - Electron II: \( n = 3, l = 2 \) → \( n + l = 3 + 2 = 5 \) - Electron III: \( n = 4, l = 1 \) → \( n + l = 4 + 1 = 5 \) ...
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