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Question
Out of the following pairs of electrons, identify the pairs of electrons present in degenerate orbitals:
| (i) | (a) `n = 3, l = 2, m_l = -2, m_s = - 1/2` |
| (b) `n = 3, l = 2, m_l = -1, m_s = - 1/2` | |
| (ii) | (a) `n = 3, l = 1, m_l = 1, m_s = + 1/2` |
| (b) `n = 3, l = 2, m_l = 1, m_s = + 1/2` | |
| (iii) | (a) `n = 4, l = 1, m_l = 1, m_s = + 1/2` |
| (b) `n = 3, l = 2, m_l = 1, m_s = + 1/2` | |
| (iv) | (a) `n = 3, l = 2, m_l = +2, m_s = - 1/2` |
| (b) `n = 3, l = 2, m_l = +2, m_s = + 1/2` |
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Solution
| (i) | (a) `n = 3, l = 2, m_l = -2, m_s = - 1/2` |
| (b) `n = 3, l = 2, m_l = -1, m_s = - 1/2` | |
| (iv) | (a) `n = 3, l = 2, m_l = +2, m_s = - 1/2` |
| (b) `n = 3, l = 2, m_l = +2, m_s = + 1/2` |
Explanation:
In a multi-electron atomic system the energy of an electron depends not only on its principal quantum number (shell), but also on its azimuthal quantum number (subshell). Electrons having the same shells and same subshells have the same energy and they are known as degenerate orbitals.
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