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What are the possible set of quantum num...

What are the possible set of quantum number for highest energy electron (in ground state) for chlorine atom.
`{:(,n,l,m,),((A),2,0,0,),((B),2,1,-2,),((C),3,1,2,),((D),3,1,0,):}`

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To determine the possible set of quantum numbers for the highest energy electron in the ground state of a chlorine atom, we need to analyze the quantum numbers provided in the options. ### Step-by-Step Solution: 1. **Identify the Atomic Number of Chlorine**: Chlorine has an atomic number of 17, which means it has 17 electrons in its neutral state. 2. **Electron Configuration of Chlorine**: The electron configuration for chlorine is: \[ 1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^5 \] This indicates that the highest energy electrons are in the 3rd shell (n = 3). 3. **Determine the Highest Energy Electrons**: The highest energy electrons in the ground state of chlorine are the 3s and 3p electrons. The 3p subshell has the highest energy among these, as it is partially filled. 4. **Quantum Numbers Definition**: Each electron in an atom is described by four quantum numbers: - **n**: Principal quantum number (energy level) - **l**: Azimuthal quantum number (subshell) - **m**: Magnetic quantum number (orientation of the orbital) - **s**: Spin quantum number (spin of the electron) 5. **Evaluate the Options**: - **Option A**: (2, 0, 0) - n = 2, l = 0 (1s subshell) - Not the highest energy. - **Option B**: (2, 1, -2) - n = 2, l = 1 (2p subshell) - Not the highest energy. - **Option C**: (3, 1, 2) - n = 3, l = 1 (3p subshell) - Invalid because m must be between -l and +l (for l = 1, m can be -1, 0, +1). - **Option D**: (3, 1, 0) - n = 3, l = 1 (3p subshell), m = 0 - Valid and represents one of the highest energy electrons. 6. **Conclusion**: The correct set of quantum numbers for the highest energy electron in the ground state of a chlorine atom is **Option D: (3, 1, 0)**.
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