The anomalous Zeeman effect arises due to
A Nuclear spin
B Electron spin and spin–orbit coupling
C Phonons
D Thermal agitation
In presence of magnetic field, energy splitting is proportional to
A B²
B B
C 1/B
D Constant
ΔE = μ_B g m_j B.
Paschen–Back effect occurs when
A Weak magnetic fields
B Very strong magnetic fields break LS coupling
C No magnetic field
D Very low temperature
Hyperfine structure splitting mainly results from
A Vibrational motion
B Electron–electron repulsion
C Interaction between electron magnetic moment and nuclear spin
D Compton scattering
The nuclear spin quantum number for a proton is
A 0
B 1/2
C 1
D 3/2
In LS coupling (Russell–Saunders), L and S combine to give
A j = L + S only
B j = L − S only
C j = L ± S
D j = L × S
The Lande g-factor depends on
A n only
B l, s, j
C m only
D Temperature
For spin–orbit coupling, interaction energy varies as
A L⋅S\mathbf{L} \cdot \mathbf{S}L⋅S
B L2L^2L2
C S2S^2S2
D L+SL + SL+S
The fine structure of hydrogen energy levels arises from
A Relativistic kinetic correction
B Spin–orbit coupling
C Darwin term
D All of the above
In hydrogen, 2P₁/₂ and 2S₁/₂ levels differ in energy due to
A Fine structure
B Lamb shift
C Hyperfine structure
D Zeeman splitting
Lamb shift provides evidence for
A Classical theory
B Dirac equation exactness
C Quantum electrodynamics (vacuum fluctuations)
D Zero-point motion only
Pauli exclusion principle ensures
A Two electrons can share all four quantum numbers
B No two electrons have identical sets of quantum numbers
C All electrons must be paired
D Orbitals collapse
Symmetry of fermion wavefunction under particle exchange is
A Symmetric
B Antisymmetric
C Arbitrary
D Undefined
Symmetry of boson wavefunctions under exchange is
A Antisymmetric
B Symmetric
C Undefined
D Always zero
When two identical fermions are exchanged, the total wavefunction changes sign because
A Their mass differs
B It is a fundamental postulate (antisymmetry requirement)
C Photons cause interference
D Orbitals collapse
In multi-electron atoms, shielding causes the energy levels to
A Become degenerate
B Separate based on penetration and screening
C Not change
D Merge together
Electron penetration order is
A s > p > d > f
B f > d > p > s
C p > s > d > f
D s = p = d
s-orbitals penetrate nucleus most strongly.
Aufbau principle fills orbitals in order of
A Increasing n only
B Increasing l only
C Increasing (n + l)
D Decreasing (n + l)
Hund’s rule maximizes
A Orbital number
B Spin multiplicity
C Nuclear charge
D Pauli violation
A closed electron shell corresponds to
A Maximum energy
B Minimum energy (stable configuration)
C Infinite degeneracy
D No spin
The jj-coupling scheme is appropriate for
A Light atoms
B Heavy atoms
C Hydrogen atom
D Ionized gases only
In jj-coupling, each electron’s total angular momentum j couples to form
A L only
B S only
C J total
D Zero
A particle with spin 0 obeys
A Fermi–Dirac statistics
B Bose–Einstein statistics
C Maxwell–Boltzmann statistics only
D None
A neutron has spin
A 0
B 1/2
C 1
D 3/2
Electron in hydrogen with quantum numbers (n=3, l=2, m=2) has how many possible spin states?
A 1
B 2
C 3
D 5
m_s = ±1/2.
For hydrogen, degeneracy between 2S and 2P states is removed primarily by
A Spin–orbit coupling
B Electron–electron interactions
C Lamb shift
D Zeeman effect
Spin–orbit coupling increases with
A Decreasing Z
B Increasing Z
C Decreasing mass
D Decreasing nuclear charge
Zeeman splitting energy shift is
A ΔE=msB\Delta E = m_s BΔE=msB
B ΔE=μBgmjB\Delta E = \mu_B g m_j BΔE=μBgmjB
C ΔE=kT\Delta E = kTΔE=kT
D Zero
The selection rule for total angular momentum j during transitions is
A Δj = 0 only
B Δj = ±1, 0 (but not 0→0)
C Δj arbitrary
D Δj = ±2
Hyperfine levels split according to
A Total electron angular momentum J and nuclear spin I
B Orbital only
C Spin only
D Nuclear charge only
The Compton shift depends on
A Wavelength only
B Scattering angle only
C Both wavelength and angle
D Only mass of electron
Δλ = (h/mc)(1 − cosθ).
Electrons show diffraction because
A They are waves only
B Their de Broglie wavelength becomes comparable to slit spacing
C They are massless
D They move slowly
The uncertainty principle forbids
A Exact simultaneous values of x and p
B Approximate measurement of both
C Any measurement
D Measuring energy
A normalized wavefunction must satisfy
A ∫ψ dx = 1
B ∫|ψ|² dx = 1
C ψ = 0
D ∫ψ dx = 0
The probability of tunneling increases when
A Barrier width increases
B Barrier height increases
C Particle energy increases
D Mass increases
A free particle has energy spectrum that is
A Discrete
B Continuous
C Zero
D Infinite
Stationary states have
A Time-varying probability distribution
B Time-independent probability density
C No normalization
D Zero momentum
A bound state wavefunction must
A Diverge at infinity
B Approach zero as x → ±∞
C Be constant
D Be imaginary
In a magnetic field, spin precession frequency is given by
A Cyclotron frequency
B Larmor frequency
C Zeeman frequency
D Raman frequency
Larmor frequency is proportional to
A Spin only
B B-field only
C Both magnetic field and gyromagnetic ratio
D Wavelength
The expectation value of position in stationary state
A Constant in time
B Oscillates
C Diverges
D Zero only
Total number of states in n=3 hydrogen shell is
A 9
B 18
C 2n² = 18
D 3
Electron probability density for s-orbitals is
A Zero at nucleus
B Maximum at nucleus
C Oscillatory at nucleus
D Undefined
A classical particle cannot be in a region where
A V > E
B V < E
C V = 0
D It never moves
Quantum particle can tunnel into V>E, classical cannot.
Pauli paramagnetism arises from
A Electron motion only
B Spin alignment of free electrons
C Nuclei rotating
D Ion movement
Landé g-factor reduces to g = 1 for
A j = l + 1/2
B j = l − 1/2
C S = 0 (normal Zeeman effect)
D P orbitals
Degeneracy of m_j levels in magnetic field is
A Lifted
B Unchanged
C Increased
D Doubled
Spin polarization occurs when
A Electrons align their orbital motion
B Spins align due to magnetic field
C Electrons stop moving
D Photons scatter
The Darwin term corrects for
A Nuclear size
B Zitterbewegung / relativistic smearing of electron position
C Electron spin being zero
D Orbital collapse
Fine structure constant α ≈ 1/137 represents
A Strength of nuclear force
B Strength of electromagnetic interaction
C Strength of gravity
D Mass ratio of electron to proton