In a simple cubic crystal, the number of atoms per unit cell is
A 2
B 4
C 1
D 8
A simple cubic lattice has 8 corner atoms each sharing 1/8 → total 1 atom.
Miller indices (h k l) represent planes with intercepts
A h/a, k/b, l/c
B a/h, b/k, c/l
C ha, kb, lc
D abc/hkl
Miller indices are the reciprocals of fractional intercepts.
The first Brillouin zone is defined as
A The smallest real-space unit cell
B The largest reciprocal-space shell
C The Wigner–Seitz cell in reciprocal space
D A sphere around k = 0
The first Brillouin zone is the Wigner–Seitz cell in k-space.
Bragg’s law is nλ = 2d sinθ. Here d represents
A Density of atoms
B Interatomic spacing
C Spacing between reflecting planes
D Distance between unit cells
d is the interplanar spacing responsible for constructive interference.
In the Einstein model of specific heat, atoms are assumed to
A Vibrate with a single frequency
B Vibrate with many frequencies
C Remain static
D Move freely
Einstein assumed all atoms oscillate with one quantized frequency.
According to Debye theory, low-temperature specific heat varies as
A T
B T²
C T³
D 1/T³
Debye model predicts Cv ∝ T³ at low temperatures.
The Fermi energy of a free electron gas depends on
A Temperature
B Lattice constant
C Electron density
D Crystal symmetry
EF ∝ n^(2/3).
The energy gap in a semiconductor is the difference between
A Core level and valence band
B Conduction band and Fermi energy
C Valence band and conduction band
D Core band and conduction band
Band gap is Ec − Ev.
A Type II superconductor is characterized by
A No Meissner effect
B Mixed state with vortices
C Only one critical field
D No flux penetration
Type II superconductors have a vortex state between Hc1 and Hc2.
The depletion width in a p–n junction increases when
A Forward bias is applied
B Doping level decreases
C Temperature increases
D Minority carriers increase
Lower doping → wider depletion region.
A Zener diode is commonly used for
A High-frequency switching
B Voltage amplification
C Voltage regulation
D Increasing current gain
Zener diodes maintain a constant output voltage in breakdown.
A bridge rectifier uses how many diodes?
A 1
B 2
C 3
D 4
Four diodes create a full-wave rectifier.
The current gain β of a BJT is defined as
A Ic/Ib
B Ic/Ie
C Ib/Ic
D Ie/Ib
β = Ic/Ib.
MOSFET operation is controlled by
A Base current
B Electric field
C Hole injection
D Impurity diffusion
MOSFETs are voltage-controlled via electric field at the gate.
Negative feedback in an amplifier generally
A Increases gain
B Causes oscillation
C Reduces distortion and improves stability
D Reduces bandwidth
Negative feedback stabilizes gain and lowers distortion.
Nuclear radius varies as
A A
B A⁰
C A¹
D A^(1/3)
R = R₀A^(1/3).
Alpha decay changes the mass number and atomic number by
A –4 and –2
B –2 and –4
C –1 and –2
D –3 and –1
Alpha particle = ⁴₂He.
A nuclear reaction with Q > 0 is
A Endothermic
B Exothermic
C Forbidden
D Independent of energy
Positive Q means energy is released.
A Geiger–Müller counter works on
A Scintillation
B Semiconductor junctions
C Gas ionization avalanche
D Photomultiplier effect
GM tubes produce Townsend avalanches.
The quark composition of a proton is
A ddu
B uds
C udd
D uud
Proton = uud.
Which decay is forbidden by lepton number conservation?
A μ⁻ → e⁻ + γ
B μ⁻ → e⁻ + νₘ̄ + νₑ
C τ⁻ → μ⁻ + ν̄ₘ + ν_τ
D n → p + e⁻ + ν̄ₑ
μ → eγ violates lepton-flavor conservation.
The Fermi surface separates
A valence and conduction bands
B electrons and holes
C occupied and unoccupied k-states at T = 0
D metals and insulators
It is the boundary of occupied electron states.
Increasing X-ray wavelength in Bragg diffraction shifts peaks to
A Lower θ
B No shift
C Higher θ
D Zero intensity
sinθ ∝ λ.
Reciprocal lattice vectors satisfy
A G·R = 0
B e^(iG·R) = 1
C G = 0
D G = 2πR
Reciprocal lattice ensures periodicity.
Debye frequency corresponds to
A Lowest phonon frequency
B Average phonon energy
C Maximum phonon frequency
D Random phonon distribution
ω_D is the cutoff frequency ensuring correct mode count.
In a direct band gap semiconductor, optical transitions
A Require phonons
B Do not conserve momentum
C Conserve momentum directly
D Are forbidden
Conduction-band minimum and valence-band maximum align in k-space.
Forward bias on p–n junction does what?
A Increases barrier
B Widens depletion
C Reduces barrier potential
D Eliminates carriers
Forward bias lowers built-in potential.
A clamping circuit uses
A Resistors only
B Inductors only
C Diodes and capacitors
D Transistors only
Diode-capacitor networks shift waveform offsets.
Small-signal amplifier analysis uses
A Large-signal models
B No bias
C Linearization around bias point
D High-power operation
Small-signal approximations require biasing.
According to BCS theory, superconductivity arises due to
A Ion pairing
B Cooper pair formation
C Free electrons
D Phonon decay
Electron pairs condense into a superfluid state.
Lorentz factor γ is equal to
A 1/(1 – v)
B √(1 – v²/c²)
C 1/√(1 – v²/c²)
D v/c
γ = 1 / √(1 − v²/c²).
Beta-minus decay emits
A Positron + neutrino
B Electron only
C Neutrino only
D Electron + antineutrino
n → p + e⁻ + ν̄ₑ.
Nuclear magic numbers include
A 2, 8, 20, 28, 50, 82, 126
B 5, 7, 9, 11
C 3, 6, 12, 24
D 4, 10, 14, 18
These correspond to filled nuclear shells.
Rutherford scattering cross-section varies as
A 1/θ
B 1/θ²
C 1/sin⁴(θ/2)
D sin(θ/2)
Rutherford formula ∝ 1/sin⁴(θ/2).
A cyclotron accelerates particles using
A Only electric field
B Only magnetic field
C Alternating E-field + constant B-field
D Gamma rays
E accelerates; B bends trajectories.
Mesons are made of
A 3 quarks
B 2 quarks
C Quark + antiquark
D 3 antiquarks
Mesons = q q̄.
Parity (P) operation reverses
A Charge
B Spin
C Time
D Spatial coordinates
Parity means r → −r.
The (010) plane is parallel to
A xy plane
B xz plane
C yz plane
D None
(010) plane intercepts only y-axis.
Packing fraction of FCC lattice is approximately
A 0.52
B 0.60
C 0.74
D 0.90
FCC is closest packed with 74% packing.
Intrinsic semiconductor conductivity depends primarily on
A Impurity atoms
B Crystal defects
C Band gap and temperature
D Lattice constant
ni ∝ exp(–Eg/2kT).
Mobility μ is defined as
A v_d / E
B E / v_d
C J / E
D E / J
μ = drift velocity / electric field.
Zener breakdown occurs due to
A Heat
B Carrier drift
C Strong electric-field tunneling
D Radiation
High field → quantum tunneling.
A common-emitter amplifier
A Does not amplify
B Provides no phase shift
C Inverts phase
D Is used as rectifier
CE amplifier gives 180° phase shift.
FETs are
A Current-controlled
B Temperature-controlled
C Voltage-controlled
D Pressure-controlled
Gate voltage controls channel.
Meissner effect refers to
A Flux trapping
B Flux penetration
C Flux expulsion
D Flux amplification
Superconductors expel magnetic flux.
Density of states (3D free electron) varies as
A 1/E
B E
C √E
D E²
g(E) ∝ √E.
Laue diffraction method relies on
A Single wavelength
B Powder
C Continuous X-ray spectrum
D No scattering
Laue uses polychromatic X-rays.
Reverse-bias current in a diode is mainly due to
A Majority carriers
B Recombination
C Minority carriers
D Avalanche region
Minority carriers dominate leakage.
Negative feedback in op-amp
A Reduces input impedance
B Increases distortion
C Improves stability
D Increases noise
Negative feedback stabilizes circuit response.
Chain reaction in fission requires the number of neutrons produced per fission to be
A Less than 1
B Equal to 0
C Equal to 1
D ≥ 1
To sustain reaction, reproduction factor ≥ 1.