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Tuesday, 17 August 2021

Problem set 97

  1. In the context of small oscillations, which one of the following does NOT apply to the normal coordinates?
    1. Each normal coordinate has an eigen-frequency associated with it
    2. The normal coordinates are orthogonal to one another
    3. The normal coordinates are all independent
    4. The potential energy of the system is a sum of squares of the normal coordinates with constant coefficients
  2. The eigenvalues of a Hermitian matrix are all
    1. real
    2. imaginary
    3. of modulus one
    4. real and positive
  3. Given the following table,
    Group-I
    P. Stem-Gerlach experiment
    Q. Zeeman effect
    R. Frank-Hertz experiment
    S. Davisson-Germer experiment
    Group-II
    1. Wave nature of particles
    2. Quantization of energy of electrons in the atoms
    3. Existence of electron spin
    4. Space quantization of angular momentum
    Which one of the following correctly matches the experiments from Group-I to their inferences in Group-II ?
    1. P-2, Q-3, R-4, S-1
    2. P-1, Q-3, R-2, S-4
    3. P-3, Q-4, R-2, S-1
    4. P-2, Q-1, R-4, S-3
  4. Which of the following atoms cannot exhibit Bose-Einstein condensation, even in principle?
    1. $^{1}H_1$
    2. $^{4}H_2$
    3. $^{23}Na_{11}$
    4. $^{30}K_{19}$
  5. Two gases separated by an impermeable but movable partition are allowed to freely exchange energy. At equilibrium, the two sides will have the same
    1. pressure and temperature.
    2. volume and temperature.
    3. pressure and volume.
    4. volume and energy.

Friday, 24 November 2017

Problem set 96

  1. The transient response of an electronic circuit is tested by giving the following wave form at the input:
    1. Sinusoidal
    2. Square
    3. Triangular
    4. Saw-tooth
  2. Which of the following effects manifests particle nature of light?
    1. Photo electric effect
    2. Blackbody radiation
    3. Interference
    4. Diffraction
  3. A ruled grating having 1000 grooves per mm is used for diffraction. If light of wavelength 300 nm is incident at right angle and if $\theta$ is the diffraction angle, $\sin\theta$ for first order diffraction will be equal to:
    1. 0.1
    2. 0.3
    3. 0.2
    4. 0.5
  4. The conventional unit cell of a body-centered cubic Bravais lattice is shown in the figure above. The conventional cell has volume $a^3$. What is the volume of the primitive unit cell?
    1. $\frac{a^3}{8}$
    2. $\frac{a^3}{4}$
    3. $\frac{a^3}{2}$
    4. $a^3$
  5. If the absolute temperature of a blackbody is increased by a factor of 3, the energy radiated per second per unit area does which of the following
    1. Decreases by a factor of 81.
    2. Decreases by a factor of 9.
    3. Increases by a factor of 9.
    4. Increases by a factor of 81.