Consider the following pairs of electrons characterized by their quantum numbers: (A) n=3, l=0, m_l=0 and n=3, l=1, m_l=0 (B) n=3, l=1, m_l=-1 and n=3, l=1, m_l=+1 (C) n=4, l=0, m_l=0 and n=3, l=2, m_l=0 (D) n=2, l=0, m_l=0 and n=3, l=0, m_l=0 Which of the above pairs of electrons occupies orbitals that are degenerate in a hydrogen atom but non-degenerate in a helium atom?

Step-by-step solution

In a single-electron species like the hydrogen atom, the energy of an orbital depends only on the principal quantum number ( n ). Therefore, orbitals with the same n value are degenerate, regardless of their azimuthal quantum number ( l ). In a multi-electron atom like helium, the energy of an orbital depends on both n and l . Pair (A) has the same n ( n=3 ) but different l ( l=0 and l=1 ). Thus, they are degenerate in hydrogen but non-degenerate in helium. Pair (B) has the same n and l , so they are degenerate in