Chapter 10: Modern Physics – Quantum Mechanics & Atomic Structure (Set-1)

The photoelectric effect demonstrates that light

A Is purely a wave

B Has particle-like properties (photons)

C Is longitudinal

D Cannot transfer energy

In the photoelectric effect, increasing the intensity (at fixed frequency above cutoff) primarily increases

A Stopping potential

B Number of emitted electrons (photoelectron current)

C Kinetic energy of each electron

D Work function

Threshold frequency in photoelectric effect depends on

A Intensity of incident light

B Work function of the material

C Electron charge only

D Distance to the source

Einstein’s photoelectric equation is

A KE=hνKE = h\nuKE=hν

B KEmax=hν−ϕKE_{max} = h\nu – \phiKEmax=hν−ϕ

C ϕ=h/ν\phi = h/\nuϕ=h/ν

D KEmax=ϕ−hνKE_{max} = \phi – h\nuKEmax=ϕ−hν

The Compton effect demonstrates that X-rays scatter off electrons with

A No change in wavelength

B Shift to longer wavelength depending on scattering angle

C Shorter wavelength always

D Total absorption only

Compton scattering treated X-ray as a particle colliding with an electron and uses

A Conservation of charge

B Conservation of mass only

C Conservation of energy and momentum

D Maxwell’s equations alone

The de Broglie wavelength of a particle is given by

A λ=h/p\lambda = h/pλ=h/p

B λ=p/h\lambda = p/hλ=p/h

C λ=hE\lambda = hEλ=hE

D λ=2πp\lambda = 2\pi pλ=2πp

Electrons accelerated through a potential V acquire de Broglie wavelength approximately

A λ=h/2meeV\lambda = h/\sqrt{2m_e eV}λ=h/2meeV

B λ=2meeV/h\lambda = \sqrt{2m_e eV}/hλ=2meeV/h

C λ=heV\lambda = h eVλ=heV

D λ=0\lambda = 0λ=0

Wave–particle duality implies that matter displays

A Only wave properties at macroscopic scales

B Both wave and particle behavior depending on experiment

C Particle behavior always

D No measurable quantum effects

Heisenberg uncertainty principle relates uncertainties Δx\Delta xΔx and Δp\Delta pΔp by

A Δx Δp≥0\Delta x\,\Delta p \ge 0ΔxΔp≥0

B Δx Δp≤ℏ/2\Delta x\,\Delta p \le \hbar/2ΔxΔp≤ℏ/2

C Δx Δp≥ℏ/2\Delta x\,\Delta p \ge \hbar/2ΔxΔp≥ℏ/2

D Δx Δp=0\Delta x\,\Delta p = 0ΔxΔp=0

A consequence of the uncertainty principle is that a particle localized very tightly in space has

A Very small momentum spread

B Very large momentum spread

C Definite momentum

D Infinite position uncertainty

The time-dependent Schrödinger equation (TDSE) for a particle is linear and first-order in

A Time derivative and second-order in spatial derivatives

B Second-order in time only

C Nonlinear in ψ

D Independent of potential

The stationary (time-independent) Schrödinger equation applies when

A The potential is time-dependent

B Looking for energy eigenstates in time-independent potential

C For relativistic particles only

D Only for photons

The wavefunction ψ(x,t)\psi(x,t)ψ(x,t) is normalized so that

A ∫∣ψ∣2 dx=0\int |\psi|^2 \,dx = 0∫∣ψ∣2dx=0

B ∫∣ψ∣2 dx=1\int |\psi|^2 \,dx = 1∫∣ψ∣2dx=1

C ψ=0\psi = 0ψ=0 everywhere

D ∫ψ dx=1\int \psi \,dx = 1∫ψdx=1

For an infinite square well of width aaa, allowed energies vary as

A nnn

B n2n^2n2

C 1/n1/n1/n

D Continuous

Boundary conditions for wavefunctions at an infinite potential wall require

A ψ finite but derivative infinite

B ψ = 0 at the wall

C ψ derivative zero at the wall

D No restriction

The probability current density j\mathbf{j}j measures

A Rate of change of probability in space (flow of probability)

B Electric current only

C Magnetic field

D Energy density

Expectation value of an observable O^\hat{O}O^ in state ψ is given by

A ⟨O^⟩=∫ψ∗O^ψ dx\langle \hat{O} \rangle = \int \psi^* \hat{O} \psi \,dx⟨O^⟩=∫ψ∗O^ψdx

B O^ψ\hat{O}\psiO^ψ only

C ∫ψ dx\int \psi \,dx∫ψdx

D None of these

Operators corresponding to observables must be

A Anti-Hermitian

B Hermitian (self-adjoint)

C Unitary only

D Nonlinear

If two operators commute, their observables can be

A Measured simultaneously with definite values (common eigenstates)

B Never measured together

C Only measured approximately

D Non-physical

The angular momentum operator L^2\hat{L}^2L^2 eigenvalues are ℏ2l(l+1)\hbar^2 l(l+1)ℏ2l(l+1). The quantum number l can be

A Any real number

B Integer ≥ 0

C Only 0 or 1

D Negative integers only

The z-component LzL_zLz has eigenvalues mℏm\hbarmℏ where m takes values

A From −l to +l in integer steps

B Any real number

C Only ±l

D Fractional multiples of ℏ only

Spin is an intrinsic form of angular momentum; electron spin quantum number s equals

A 0

B 1/2

C 1

D 3/2

Magnetic moment associated with electron spin gives rise to

A No interaction with magnetic field

B Interaction μ⋅B\mu\cdot Bμ⋅B causing energy splitting

C Only electric effects

D Infinite energy

Stern–Gerlach experiment demonstrated quantization of

A Charge

B Angular momentum (space quantization of magnetic moment)

C Mass

D Light intensity

In a Stern–Gerlach apparatus with silver atoms, the beam splits into two because

A Silver atoms are neutral overall

B Silver has a single unpaired electron (spin-1/2) giving two spin states

C Magnetic field is uniform

D Atoms ionize

Pauli exclusion principle states that no two electrons in an atom can have the same set of

A Energy only

B Four quantum numbers (n, l, m, s)

C Spin only

D Position only

The Zeeman effect is the splitting of spectral lines in presence of

A Electric field only

B Magnetic field

C Gravitational field

D Temperature change

In weak-field (normal) Zeeman effect, spectral lines split into

A A single line only

B Three components (triplet) with spacing proportional to B

C Infinite components

D Two components only

Spin–orbit coupling arises from interaction between electron spin and its motion around nucleus, effectively producing

A An electric field at electron rest frame

B A magnetic field in electron rest frame that couples with spin magnetic moment

C No interaction

D Nuclear spin flip only

Fine structure in atomic spectra arises due to combination of relativistic correction to kinetic energy, spin–orbit coupling, and

A Photoelectric effect

B Lamb shift only

C Darwin term and other small corrections (including relativistic)

D Classical thermal effects

The spin quantum number s for an electron allows two possible msm_sms values:

A −1, 0, +1

B −1/2 and +1/2

C 0 only

D Any integer

The hydrogen atom energy levels from Schrödinger equation (non-relativistic) depend on principal quantum number n as

A En∝nE_n \propto nEn∝n

B En∝1/n2E_n \propto 1/n^2En∝1/n2

C En∝n2E_n \propto n^2En∝n2

D Continuous spectrum only

Radial wavefunctions for hydrogen are characterized by nodes; number of radial nodes equals

A n

B n − l − 1

C l

D 0 always

The ladder (raising and lowering) operators L+,L−L_+ , L_-L+,L− act on spherical harmonics to change

A n quantum number

B m quantum number by ±1

C l by ±1

D Energy by large amounts

A normalized wavefunction squared gives

A Probability density of finding particle at a point

B Potential energy

C Momentum directly

D Temperature distribution

Quantum tunneling is a phenomenon where a particle

A Is reflected with probability 1 if barrier > energy

B Has finite probability to penetrate and cross a classically forbidden potential barrier

C Can never escape bound states

D Always loses energy crossing barrier

In alpha decay, tunneling through Coulomb barrier explains

A Why alpha particles are never emitted

B The finite lifetime and decay rates despite classically forbidden escape

C Conservation of momentum violation

D Creation of alpha particles from vacuum

Nodes in standing matter waves correspond to positions where probability density is

A Maximum

B Zero

C Negative

D Undefined

Time evolution of a stationary state ψn(x)e−iEnt/ℏ\psi_n(x)e^{-iE_nt/\hbar}ψn(x)e−iEnt/ℏ gives observables that are

A Time-dependent oscillating

B Time-independent expectation values

C Divergent with time

D Randomly varying

The Born interpretation assigns ∣ψ∣2|\psi|^2∣ψ∣2 as

A Energy density

B Probability density of finding the particle

C Electric field intensity

D Momentum density

Spin–orbit coupling causes splitting within otherwise degenerate levels because it depends on

A Electron charge only

B Relative orientation of spin and orbital angular momenta (j = l ± 1/2)

C Nuclear spin only

D External temperature

The total angular momentum J=L+S\mathbf{J} = \mathbf{L} + \mathbf{S}J=L+S; possible j values for electron are

A l only

B l ± 1/2

C S only

D Any integer

In LS coupling (Russell–Saunders), spin–orbit interactions are treated as

A Negligible always

B Weak compared to electrostatic interactions between electrons (good for light atoms)

C Dominant over all interactions

D Only for free electrons

Pauli exclusion principle explains the structure of periodic table because it prohibits two electrons in an atom from occupying

A The same orbital only if both are excited

B The same set of four quantum numbers simultaneously

C Same nucleus

D Different energy levels

Identical fermions (e.g., electrons) have a total wavefunction that is

A Symmetric under particle exchange

B Antisymmetric under exchange

C Neither symmetric nor antisymmetric

D Always real-valued

Bosons differ from fermions in that boson many-particle wavefunction is

A Antisymmetric under exchange

B Symmetric under exchange allowing multiple occupancy of same state

C Non-normalizable

D Forbidden by Pauli principle

Fine structure constant α\alphaα is dimensionless and approximately equal to

A 1/137

B 137

C 0

D π

The Lamb shift (not predicted by Dirac theory) arises due to

A Strong nuclear forces

B Radiative corrections from quantum electrodynamics (vacuum fluctuations)

C Classical electron orbits

D Thermal motion

Measurement in quantum mechanics causes wavefunction collapse (per Copenhagen interpretation), which implies that after a precise position measurement, the particle’s momentum becomes

A Precisely known as well

B Highly uncertain (large momentum spread)

C Zero always

D Identical to prior value

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