Assignment-I

State the four sets of quantum numbers with a precise explanation.

Differentiate orbital vs orbit in atomic theory.

Give the shapes (nodal surfaces) of 2p and 3d orbitals in words.

Define radial node and angular node, and give general formulas for each.

State the Pauli Exclusion Principle precisely.

State Hund’s rule of maximum multiplicity with examples.

Give the (n + ℓ) rule and how ties are broken in Aufbau filling.

Write the ground-state configuration of Fe (Z=26) and Fe³⁺.

For hydrogenic atoms, what is the total degeneracy of the nth level and why?

From the hydrogenic Schrödinger equation, justify allowed ℓ = 0…(n–1) and mℓ = –ℓ…0...+ℓ; hence show degeneracy n².

Show that the total node count for a hydrogenic orbital is n–1, and split it into radial = n-ℓ-1 and angular = ℓ nodes; illustrate for 2s, 3s, 3p, 3d.

Using radial probability plots, explain why the most probable radius of 1s is a₀, and how the peak shifts with n.

Explain why 4s fills before 3d in many neutral atoms, yet 4s electrons are ionized before 3d when forming cations.

Using exchange energy arguments, rationalize the extra stability of half-filled and fully filled subshells; discuss Cr and Cu anomalies.

Using the Rydberg formula, relate spectral line series (Lyman, Balmer, Paschen) to energy level differences; explain convergence to the ionization limit.

Contrast Bohr’s model with the wave-mechanical model: which phenomena force the adoption of ψ-based orbitals?

Sketch angular parts Yℓm(θ,φ) for p and d orbitals to justify the classic “dumbbell” and “cloverleaf” shapes qualitatively.

Orbitals with spherical symmetry are:  a) 2p                      b) 2s                           c) 3d                                  d) 4f

Angular nodes in 4p:                            a) 0                       b) 1                              c) 2                                   d) 3

Configuration [Ar] 3d⁵ 4s¹ corresponds to: a)Cr (ES)              b) Mn                           c) Cr(GS)                         d) Cu

Which is violated in excited O: 1s²2s²2p33s¹?         a) Hund b) Pauli                         c) Aufbau                         d) None

Orbitals in n=3 shell: a) 3                        b) 6                               c) 9                                  d) 16

Multiplicity for three unpaired electrons: a) 2       b) 3                               c) 4                                  d) 5

Energy of the electron in the first Bohr orbit of H:   a) 0 eV                 b) –13.6 eV                   c) –6.8 eV                      d) +13.6 eV

Radial nodes in 4s:                                                 a) 0                      b) 1                                c) 2                                 d) 3

Unpaired electrons in Fe²⁺ (high-spin, free ion):     a) 3     b) 4   c) 5 d) 6

Which of the following electronic transitions are allowed?  a) ns→np      b) np→nf               c) nd→nd                       d) nf→ns