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Question 1
What is the angular frequency of an ideal LC circuit?
- 1/√(LC)
- √(LC)
- 1/(LC)
- LC
Question 2
For a monatomic ideal gas, the adiabatic index γ = C_p/C_v is:
- 5/3
- 7/5
- 3/2
- 4/3
Question 3
For a diatomic ideal gas, the adiabatic index γ equals 7/5.
- True
- False
Question 4
The rest mass of the electron is approximately ______ keV/c².
Fill in the blank
Question 5
A pion is best described as which of the following?
- A meson: a boson made of a quark–antiquark pair
- A baryon made of three quarks
- A lepton, like the electron
- A massless gauge boson
Question 6
The Heisenberg uncertainty principle requires that the product ΔpΔx be at least:
- ħ/2
- ħ
- 2ħ
- 0
Question 7
Which expression correctly gives the Poynting vector?
- S = (1/μ₀)(E × B)
- S = μ₀(E × B)
- S = (1/ε₀)(E · B)
- S = ε₀(E × B)
Question 8
The cyclotron radius of a charged particle moving perpendicular to a magnetic field is:
- r = mv/(qB)
- r = qB/(mv)
- r = mvB/q
- r = qv/(mB)
Question 9
In nondegenerate perturbation theory, the first-order energy correction to state n is given by:
- E_n^(1) = ⟨φ_n^(0)|Ĥ₁|φ_n^(0)⟩
- E_n^(1) = Σ_{k≠n} |⟨φ_k^(0)|Ĥ₁|φ_n^(0)⟩|² / (E_n^(0) − E_k^(0))
- E_n^(1) = ⟨φ_n^(0)|Ĥ₀|φ_n^(0)⟩
- E_n^(1) = Ĥ₁|φ_n^(0)⟩ / E_n^(0)
Question 10
In a tube open at one end and closed at the other, the resonant wavelengths are:
- λ = 4L/(2n+1)
- λ = 2L/n
- λ = 4L/(2n)
- λ = L/n
Question 11
The electric field inside a conducting shell enclosing a neutral electric dipole is zero.
- True
- False
Question 12
Which expression gives the bound current density J_b in a magnetized material?
- J_b = ∇×M
- J_b = ∇·M
- J_b = −∇·P
- J_b = ∂P/∂t
Question 13
Which expression gives the moment of inertia of a continuous mass distribution?
- I = ∫ r² dm
- I = ∫ r dm
- I = ∫ r² dV
- I = ∫ m r² dr
Question 14
For thin-film interference at normal incidence, constructive interference occurs when:
- mλ = 2nd
- (m - 1/2)λ = 2nd
- mλ = nd
- (m + 1/2)λ = nd
Question 15
In thin-film interference, destructive interference occurs when (m - 1/2)λ = 2nd.
- True
- False
Question 16
In the photoelectric effect, the photon energy ħω equals the maximum kinetic energy T plus the ___.
Fill in the blank
Question 17
What is the mean thermal energy ⟨ε⟩ of a photon mode of frequency ω in blackbody radiation?
- ⟨ε⟩ = ħω / (e^(ħω/(k_B T)) - 1)
- ⟨ε⟩ = ħω / (e^(ħω/(k_B T)) + 1)
- ⟨ε⟩ = k_B T / (e^(ħω/(k_B T)) - 1)
- ⟨ε⟩ = ħω (e^(ħω/(k_B T)) - 1)
Question 18
Which is the Rydberg formula for the wavelength λ of a spectral line in a hydrogen-like atom?
- 1/λ = R Z² (1/n₁² - 1/n₂²)
- 1/λ = R Z (1/n₁² - 1/n₂²)
- λ = R Z² (1/n₁² - 1/n₂²)
- 1/λ = R Z² (1/n₂² - 1/n₁²)
Question 19
The ground-state energy of hydrogen (Z=1, n=1) is approximately ___ eV.
Fill in the blank
Question 20
Which of the following is NOT one of the hydrogen spectral series listed?
- Lyman
- Balmer
- Brackett
- Doppler
Question 21
Which two-spin-1/2 state is the singlet state (s=0)?
- |0,0> = (↑↓ - ↓↑)/√2
- |1,0> = (↑↓ + ↓↑)/√2
- |1,1> = ↑↑
- |1,-1> = ↓↓
Question 22
The Pauli matrix σ_z is equal to [[1,0],[0,-1]].
- True
- False
Question 23
What is the Heisenberg equation of motion for an operator O (with no explicit time dependence)?
- dO/dt = (1/(iħ)) [O, H]
- dO/dt = (1/(iħ)) [H, O]
- dO/dt = (iħ) [O, H]
- dO/dt = (1/ħ) [O, H]
Question 24
Which formula correctly gives the observed frequency f' for a moving source and observer (with v_o toward the source and v_s toward the observer)?
- f' = f₀ (v + v_o) / (v - v_s)
- f' = f₀ (v + v_s) / (v + v_o)
- f' = f₀ (v - v_o) / (v + v_s)
- f' = f₀ (v - v_s) / (v + v_o)
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