In a multielectron atom, which of the following orbitals described by three quantum numbers will have the same energy in absence of electric and magnetic fields?
A. \( n = 1, l = 0, m_l = 0 \)
B. \( n = 2, l = 0, m_l = 0 \)
C. \( n = 2, l = 1, m_l = 1 \)
D. \( n = 3, l = 2, m_l = 1 \)
E. \( n = 3, l = 2, m_l = 0 \)
Choose the correct answer from the options given below:
In a multielectron atom, which of the following orbitals described by three quantum numbers will have the same energy in absence of electric and magnetic fields?
A. \( n = 1, l = 0, m_l = 0 \)
B. \( n = 2, l = 0, m_l = 0 \)
C. \( n = 2, l = 1, m_l = 1 \)
D. \( n = 3, l = 2, m_l = 1 \)
E. \( n = 3, l = 2, m_l = 0 \)
Choose the correct answer from the options given below:
Show Hint
- D and E Only
- C and D Only
- B and C Only
- A and B Only
The Correct Option is A
Solution and Explanation
In the absence of electric and magnetic fields, the energy of orbitals depends only on the principal quantum number \(n\) for a hydrogen-like atom.
Step 1: For multielectron atoms, the energy levels are further split due to electron-electron interactions and quantum numbers \(l\) and \(m_l\).
Step 2: Orbitals with the same \(n\) but different \(l\) and \(m_l\) have the same energy due to the degeneracy of the \(n\) level.
Final Conclusion: The correct answer is Option (1), where D and E have the same energy.
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A. \( n = 1, l = 0, m_l = 0 \)
B. \( n = 2, l = 0, m_l = 0 \)
C. \( n = 2, l = 1, m_l = 1 \)
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Choose the correct answer from the options given below: Given below are two statements:
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