In the photoelectric effect, stopping potential is directly related to
A Intensity of incident light
B Wavelength
C Maximum kinetic energy of photoelectrons
D Number of photons per second
eV0=KEmaxeV_0 = KE_{\max}eV0=KEmax.
When the frequency of light increases above threshold frequency, the photoelectric current
A Increases
B Decreases
C Remains constant
D Drops to zero
Current depends on intensity; KE depends on frequency.
Work function of a metal is
A KE of fastest electron
B Minimum energy to free an electron
C Threshold intensity
D Proportional to current
Photoelectric emission happens instantaneously because
A Electrons travel at speed of light
B The photon energy is delivered in a single quantum
C Photons accumulate energy over time
D Metal expands
Compton shift is maximum when the photon scattering angle is
A 0°
B 45°
C 90°
D 180°
Δλmax=2hmec\Delta\lambda_{\max} = \frac{2h}{m_e c}Δλmax=mec2h.
If the scattering angle in Compton effect is zero, the wavelength change is
A Maximum
B Minimum (zero)
C Negative
D Infinite
Compton wavelength of an electron is
A h/meh/m_eh/me
B h/(mec)h/(m_e c)h/(mec)
C hc/mehc/m_ehc/me
D e/mee/m_ee/me
Compton effect cannot be observed using visible light because
A Visible light is incoherent
B Electron mass is too small
C Wavelength shift is too small to detect
D Scattering does not occur
De Broglie wavelength for a macroscopic object is negligible because
A Wavelength is inversely proportional to momentum
B h is small
C Object velocity is zero
D Object absorbs the wave
Electron diffraction experiments confirmed
A Electrons have no mass
B Electrons behave only like particles
C Matter has wave nature
D Classical physics is perfect
De Broglie wavelength of a particle increases when
A Momentum increases
B Momentum decreases
C Velocity increases
D Mass increases
A particle confined in a small region has
A Small uncertainty in momentum
B Large uncertainty in momentum
C No uncertainty
D Zero kinetic energy
Δx↓⇒Δp↑\Delta x \downarrow \Rightarrow \Delta p \uparrowΔx↓⇒Δp↑.
Uncertainty relation between energy and time is
A ΔEΔt=0\Delta E \Delta t = 0ΔEΔt=0
B ΔEΔt≥ℏ/2\Delta E \Delta t \ge \hbar/2ΔEΔt≥ℏ/2
C ΔEΔt≤ℏ\Delta E \Delta t \le \hbarΔEΔt≤ℏ
D No such relation
The Schrödinger equation is
A Relativistic
B Classical
C Non-relativistic wave equation for quantum mechanics
D Newton’s law
In a bound state, the energy levels of a particle are
A Continuous
B Discrete
C Infinite
D Arbitrary
The ground state energy in an infinite potential well is
A Zero
B Negative
C Non-zero
D Infinite
Zero-point energy exists — cannot be zero.
In quantum mechanics, potential steps can cause
A Reflection even when energy > potential
B Never reflection
C Spontaneous emission
D No change in wavefunction
Particle tunneling probability decreases when
A Barrier width decreases
B Barrier height increases
C Particle energy increases
D Wavelength increases
The expectation value of momentum ⟨p⟩\langle p \rangle⟨p⟩ is
A Always zero
B ∫ψ*(−iħ d/dx)ψ dx
C ∫ψ dx
D Defined only for free particle
A wavefunction must be
A Finite, single-valued, normalizable
B Multi-valued
C Infinite at boundaries
D Purely imaginary
Quantum state degeneracy means
A No wavefunction exists
B Different states have same energy
C Energy levels destroyed
D Spin disappears
In a harmonic oscillator, energy levels are
A equally spaced
B random
C proportional to n²
D zero only
Zero-point energy of harmonic oscillator equals
A 0
B hνh\nuhν
C 12hν\frac{1}{2}h\nu21hν
D 2hν2h\nu2hν
Allowed angular momentum values are
A L=nℏL = n\hbarL=nℏ
B l(l+1)ℏ\sqrt{l(l+1)}\hbarl(l+1)ℏ
C (2n+1)ℏ(2n+1)\hbar(2n+1)ℏ
D Zero only
A magnetic moment interacts with magnetic field through energy
A μ+B\mu + Bμ+B
B μB\mu BμB
C μ⃗⋅B⃗\vec{\mu}\cdot\vec{B}μ⋅B
D μ/B\mu/Bμ/B
Electron spin quantum number takes values
A 0
B 1
C 1/2
D 3/2
The Stern–Gerlach experiment proved
A Electrons have continuous angular momentum
B Space quantization of spin
C Photons have mass
D Magnetic fields quantize charges
Silver atoms split into two beams in Stern–Gerlach because
A They ionize
B They have one unpaired electron (spin 1/2)
C They are heated
D They are paramagnetic
Pauli exclusion principle applies to
A Bosons
B Fermions
C Photons
D All particles
Pauli exclusion causes electrons in atoms to
A All occupy same level
B Fill levels in increasing energy order
C Have same spin always
D Jump randomly
Zeeman effect occurs due to
A Electric field
B Magnetic field interaction with magnetic dipole moment
C Vibrations of atoms
D Pressure
Normal Zeeman effect splits a spectral line into
A One line
B Two lines
C Three equally spaced lines
D Infinite lines
Anomalous Zeeman effect is due to
A Zero spin
B Electron spin and spin–orbit coupling
C Electric dipole
D Low temperature
Spin–orbit coupling energy is proportional to
A L·S
B L + S
C n
D Mass
Fine structure arises due to
A Nuclear spin only
B Relativistic correction + spin–orbit coupling + Darwin term
C External fields
D Phonons
Hydrogen atom degeneracy is removed by
A Removing electrons
B Fine structure effects
C Cooling
D Pressure
A free particle solution of Schrödinger equation is
A decaying wave
B exponential growth
C plane wave ei(kx−ωt)e^{i(kx-\omega t)}ei(kx−ωt)
D delta function
Momentum operator in QM is
A −iℏddx-i\hbar \frac{d}{dx}−iℏdxd
B iℏddxi\hbar \frac{d}{dx}iℏdxd
C d2/dx2d^2/dx^2d2/dx2
D Multiplication by x
Position and momentum operators satisfy
A commute
B do not commute
C commute sometimes
D always commute squared
[x,p]=iℏ[x, p] = i\hbar[x,p]=iℏ.
The hydrogen atom magnetic quantum number m takes values
A from −l to +l
B from 0 to n
C only ±1
D always zero
Orbital angular momentum quantum number l determines
A energy always
B orbital shape
C spin
D mass of electron
For l = 2 (d orbital), number of possible m values is
A 2
B 3
C 5
D 10
m = −2, −1, 0, +1, +2.
Degeneracy of hydrogen level n is
A n
B n²
C 2n²
D 4n
Spin multiplicity is given by
A 2S
B 2S + 1
C S
D S−1
The Compton formula can be derived by assuming photons have
A Mass
B Momentum p=h/λp = h/\lambdap=h/λ
C No energy
D No momentum
Electron wavelength comparable to atomic spacing occurs at energies of
A a few eV
B keV range
C MeV
D GeV
~1 Å corresponds to ~100 eV.
Tunneling probability through a barrier is
A independent of barrier width
B exponential in width and height
C linear
D discrete
The Schrödinger equation is
A Relativistic
B Deterministic in wave evolution
C Nonlinear
D Based on classical trajectories
A wave packet spreads over time because
A Uncertainty principle
B Dispersion of component waves
C Photons interfere
D Reflection
Electrons in the same orbital must have
A Same spin
B Opposite spins
C Random spin
D No spin