問題一覧
1
In classical mechanics, which of the following is a correct interpretation of Poisson brackets?
They determine whether two classical quantities are independent conserved quantities.
2
A particle moves in a central force field with potential energy V(r)=-rk. What is the nature of its motion according to classical mechanics?
The motion can be either bounded (elliptical) or unbounded (parabolic/hyperbolic) depending on energy. The motion is completely independent of initial conditions.
3
A block of mass m is placed on a frictionless horizontal surface and connected to a spring of force constant k. If the block is displaced by x0 and released, which of the following correctly describes its motion?
The block executes simple harmonic motion with angular frequency sqrt(k/m).
4
Which of the following observations in the photoelectric effect could not be explained by classical wave theory?
Both B and C
5
A mass-spring system with mass m and spring constant k is driven by an external force F(t) = F * 0cos(omegat) At resonance, what is the system's oscillation frequency?
w = sqrt(k/m)
6
If a flexible string is stretched under tension T and has a mass per unit length µ, the speed of wave propagation along the string is given by:
v=vsqrt(T/u)
7
Which of the following types of waves requires a medium for propagation?
Sound waves
8
A a medium has a frequency of 500 Hz and a wavelength of 2 m. What is its speed?
1000 m/s
9
The frequency of a 12C160 molecule is 6.5405 x 1013 s-1. The atomic masses are: 12C: 12.00000 amu; 13C: 13.00335 amu; 160: 15.994915 amu; 170: 16.99913 amu. Find the vibrational frequency of a 13C160 molecule, assuming that the force constant is unchanged.
v=6.401x10^13 s-1
10
The Stefan-Boltzmann law states that the total power radiated by a black body per unit area is proportional to:
T2
11
Which of the following is a direct consequence of Planck's quantization of energy?
Photoelectric effect
12
Which of the following correctly expresses the relationship between the speed of light c, its frequency f, and wavelength A?
c=λ/f
13
A car of mass m is moving along a circular track of radius R with constant speed v. What is the magnitude of the net force acting on the car?
mv³/R directed radially inward.
14
A string of length L is fixed at both ends and vibrates in the second harmonic mode. How many nodes and antinodes are present in the string?
3 nodes, 2 antinodes
15
What happens when an electron in a hydrogen atom transitions from a higher energy level (n) to a lower energy level (n.)?
A photon is emitted with energy hvwEn2-En1
16
If the tension in a stretched string is quadrupled, how does the wave speed change?
It doubles.
17
The general solution of a one-dimensional classical harmonic oscillator with mass m and force constant k is given by x(t) = A * cos(omegat + phi) What is the correct expression for the angular frequency ω?
w= sqrt(k/m)
18
A harmonic oscillator with mass m and frequency w has total energy E. What is the maximum speed of the oscillator?
vmax= sqrt(2E / m)
19
Which of the following statements best describes wave-particle duality?
Light sometimes behaves as a wave and sometimes as a particle, depending on the experiment.
20
Which of the following is true about the Hamiltonlan function in classical mechanics?
It is the total energy of the system, expressed in terms of generalized coordinates and momenta.
21
A standing wave is formed when:
Two waves of the same frequency and amplitude travel in opposite directions and interfere.
22
Which of the statements about classical wave motion is incorrect?
The amplitude of a wave is directly related to its frequency in all cases.
23
In classical wave theory, what is the significance of the intensity of an electromagnetic wave?
It is proportional to the square of the electric field amplitude.
24
A wave on a string is described by: y(x,t)=0.02sin(5x-40t) What is the wave speed?
10 m/s
25
The stopping potential in a photoelectric experiment is the potential required to:
Stop the most energetic emitted electrons from reaching the anode
26
The speed of a travelling wave is given by which equation
v=w/k
27
Bohr's model successfully explains the spectral lines of hydrogen but fails for multi-electron atoms. Why?
It does not account for electron-electron interactions in multi-electron atoms
28
A wave is travelling in the +x direction and is given by: y(x,t)=Asin(x+ut) What happens to the wave direction if the equation changes to: y(x,t)=Asin(lx-wt)
The wave reverses and moves in the -x direction.
29
A metal has a work function of 2.0 eV. If light of wavelength 400 nm is incident on it, what will be the maximum kinetic energy of the emitted electrons?
1.1 eV
30
A particle of mass m is moving under the influence of a force given by F=-kv, where k is a positive constant and v is the velocity of the particle. What is the velocity of the particle as a function of time if it starts with Initial velocity vo at t=0?
v(t) = v0e ^ (- kt / m)
31
Which of the following correctly describes the nature of the oscillating electric and magnetic fields in an electromagnetic wave?
The electric and magnetic fields oscillate perpendicular to each other and perpendicular to the direction of propagation.
32
Two bodies of masses m1 and m2 are connected by a massless string and suspended over a frictionless pulley. If m1 > m2, what is the acceleration of the system?
g (m1-m2/m1+m2)
33
In the Compton effect, when X-rays scatter off electrons, what happens to the wavelength of the X-ray photons?
It increases
34
A flexible string of length L is fixed at both ends and vibrating in its fundamental mode. What is the wavelength of the wave formed on the string?
L/2
35
Which of the ff correctly describes the principle of least action in classical mechanics?
The trajectory of a particle is the one that extremizes the action Integral.
36
The potential energy function for a one-dimensional harmonic oscillator is given by V(x) = 1/2 k x ^ 2 what position does the kinetic energy equal the potential energy?
x = A / (sqrt(3))
37
Which of the following correctly expresses Einstein's photoelectric equation?
KEmax hv-
38
According to de Broglie's hypothesis, the wavelength (A) associated with a moving particle of mass m and velocity v is given by
h/mv
39
A sinusoidal travelling wave moves in the +x direction with an amplitude of 0.05 m and a frequency of 20 Hz. If the wave speed is 5m / s_{0} what is its wavelength?
0.5 m
40
Which of the following experimental observations provided the first direct evidence of the wave nature of light?
Double-slit experiment
41
Which of the following statements about electromagnetic waves is incorrect?
Electromagnetic waves require a material medium for propagation.
42
Which phenomenon best demonstrates the particle nature of light?
Photoelectric effect
43
Which assumption in Planck's quantum hypothesis resolved the "ultraviolet catastrophe" in black-body radiation?
Energy is quantized as E-nhv, where n is an integer
44
The frequency of vibration of a 1H35CI molecule is 8.966 x 1013 s-1. What would the frequency be if the hydrogen atom were infinitely massive?
v= 1.501 x1013s - 1
45
In Bohr's model of the hydrogen atom, the quantization of electron orbits is based on which fundamental principle?
The angular momentum of the electron is an integer multiple of A (reduced Planck's constant)
46
A travelling wave is described by the equation: y(x,t) = Asin(kx-ot) What does the term k represent?
Angular wave number
47
Assume that a hydrogen atom is bonded to a large crystal with a chemical bond that is equivalent to a spring having a force constant equal to 600.0 N m-1. Assume that the hydrogen atom oscillates harmonically but the atom at the other end of the bond is stationary. Find the frequency of the oscillation.
v = 9.532 * 10115 - 1
48
A flexible string of length L is vibrating in the third harmonic mode. What is the frequency ratio between this mode and the fundamental mode?
1:3
49
For a sinusoidal wave traveling in a medium, which of the following properties remains unchanged when it moves from one medium to another?
Frequency
50
A violin string has a mass per unit length of 3gm - 1 Find the tension force necessary to produce a fundamental frequency s-1 if the length of the string is 50.0 cm.
T=585.1N
51
According to Liouville's theorem in classical mechanics, which of the following statements is correct?
The phase space volume of an ensemble of systems is conserved over time.
52
The work function ()of a metal represents:
The minimum photon energy required to eject an electron
53
Which of the following correctly describes the radius of the electron's orbit in the hydrogen atom according to Bohr's model?
rnn2r0, where ro is the Bohr radius
54
What happens to the wavelength of an electromagnetic wave when it from vacuum into a medium with refractive index n?
It decreases by a factor of n.