Match the entries in Column I with the correctly related quantum number(s) in Column II. Indicate your answer by darkening the appropriate bubbles of the 4 × 4 matrix given in the ORS.
Column I
(A) Orbital angular momentum of the electron in a hydrogen-like atomic orbital
(B) A hydrogen-like one-electron wave function obeying Pauli principle
(C) Shape, size and orientation of hydrogen-like atomic orbitals
(D) Probability density of electron at the nucleus in hydrogen-like atom
Column II
(p) Principal quantum number
(q) Azimuthal quantum number
(r) Magnetic quantum number
(s) Electron spin quantum number
Column I
(A) Orbital angular momentum of the electron in a hydrogen-like atomic orbital
(B) A hydrogen-like one-electron wave function obeying Pauli principle
(C) Shape, size and orientation of hydrogen-like atomic orbitals
(D) Probability density of electron at the nucleus in hydrogen-like atom
Column II
(p) Principal quantum number
(q) Azimuthal quantum number
(r) Magnetic quantum number
(s) Electron spin quantum number
Answer: A → II, A → III, B → I, B → II, B → III, B → IV, C → I, C → II, C → III, D → I, D → II
Solution
(A) Orbital angular momentum depends only on the azimuthal quantum number l: .
(B) The Pauli exclusion principle requires specification of all four quantum numbers including spin (s), so a complete wave function must include the spin quantum number.
(C) Shape is determined by l (azimuthal), size by n (principal), and orientation by m (magnetic). All three are needed.
(D) Probability density at the nucleus (r=0) depends on n and l. Only s-orbitals (l=0) have non-zero probability at the nucleus, and this probability varies with n. So both p and q are involved, and the orientation (r) also matters for the radial part.
(B) The Pauli exclusion principle requires specification of all four quantum numbers including spin (s), so a complete wave function must include the spin quantum number.
(C) Shape is determined by l (azimuthal), size by n (principal), and orientation by m (magnetic). All three are needed.
(D) Probability density at the nucleus (r=0) depends on n and l. Only s-orbitals (l=0) have non-zero probability at the nucleus, and this probability varies with n. So both p and q are involved, and the orientation (r) also matters for the radial part.
JEE Advanced · 2008 · 13 Apr 2008 · Paper 2 · Match the columns