Atomic And Molecular Physics MCQ

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• In a two-electron atomic system having orbital and spin angular momenta $${l_1}{l_2}$$  and $${s_1}{s_2}$$  respectively, the coupling strengths are defined as $${\Gamma _{{l_1}{l_2}}},\,{\Gamma _{{s_1}{s_2}}},\,{\Gamma _{{l_1}{s_1}}},\,{\Gamma _{{l_2}{s_2}}},\,{\Gamma _{{l_1}{l_2}}}$$      and $${\Gamma _{{l_2}{s_1}}}.$$  For the jj coupling. scheme to be applicable, the coupling strengths must satisfy the condition
  ক

  $${\Gamma _{{l_1}{l_2}}},\,{\Gamma _{{s_1}{s_2}}} > {\Gamma _{{l_1}{s_1}}},\,{\Gamma _{{l_2}{s_2}}}$$

  খ

  $${\Gamma _{{l_1}{s_1}}},\,{\Gamma _{{l_2}{s_2}}} > {\Gamma _{{l_1}{l_2}}},\,{\Gamma _{{s_1}{s_2}}}$$

  গ

  $${\Gamma _{{l_1}{s_2}}},\,{\Gamma _{{l_2}{s_1}}} > {\Gamma _{{l_1}{l_2}}},\,{\Gamma _{{s_1}{s_2}}}$$

  ঘ

  $${\Gamma _{{l_1}{s_2}}},\,{\Gamma _{{l_2}{s_1}}} > {\Gamma _{{l_1}{s_1}}},\,{\Gamma _{{l_2}{s_2}}}$$
• The target of an X-ray tube is subjected to an excitation voltage V. The wavelength of the emitted X-rays is proportional to
  ক

  $$\frac{1}{{\sqrt V }}$$

  খ

  $$\sqrt V $$

  গ

  $$\frac{1}{V}$$

  ঘ

  $$V$$
• The typical wavelengths emitted by diatomic molecules in purely vibrational and purely rotational transitions are respectively in the region of
  ক

  infrared and visible

  খ

  visible and infrared

  গ

  infrared and microwave

  ঘ

  microwave and infrared
• In the microwave spectrum of identical rigid diatomic molecules, the separation between the spectral lines is recorded to be 0.7143 cm^-1. The moment of inertia of the molecule, in kg-m² is
  ক

  2.3 × 10^-36

  খ

  2.3 × 10^-40

  গ

  7.8 × 10^-42

  ঘ

  7.8 × 10^-46
• The NMR spectrum of ethanol (CH₃CH₂OH) comprises of three bunches of spectral lines. The number of spectral lines in the bunch corresponding to CH₂ group is
  ক

  1

  খ

  2

  গ

  3

  ঘ

  4
• The D₁ and D₂ lines of Na(3²p_1/2 → 3²s_1/2, 3²p_3/2 → 3²s_1/2) will split on the application of a weak magnetic field into
  ক

  4 and 6 lines respectively

  খ

  3 lines each

  গ

  6 and 4 lines respectively

  ঘ

  6 lines each
• Assuming that the L-S coupling scheme is valid, the number of permitted transitions from ²P_3/2 to ²s_1/2 due to a weak magnetic field is
  ক

  2

  খ

  4

  গ

  6

  ঘ

  10
• The degeneracy of the spectral term ³f is
  ক

  7

  খ

  9

  গ

  15

  ঘ

  21
• The L, S and J quantum numbers corresponding to the ground state electronic configuration of boron (Z = 5) are
  ক

  L = 1, S = $$\frac{1}{2}$$, J = $$\frac{3}{2}$$

  খ

  L = 1, S = $$\frac{1}{2}$$, J = $$\frac{1}{2}$$

  গ

  L = 1, S = $$\frac{3}{2}$$, J = $$\frac{1}{2}$$

  ঘ

  L = 0, S = $$\frac{3}{2}$$, J = $$\frac{3}{2}$$
• Three consecutive absorption lines at 64.275 cm^-1, 77.130 cm^-12 and 89.985 cm^-1 have been observed in a microwave spectrum for a linear rigid diatomic molecule. The moments of inertia $${I_A}$$ and $${I_B}$$ are ($${I_A}$$ is with respect to the bond axis passing through the centre of mass and $${I_B}$$ is with respect to an axis passing through the centre of mass and perpendicular to bond axis)
  ক

  both equal to $$\frac{{{\hbar ^2}}}{{12.855\,hc}}$$  g-cm²

  খ

  zero and $$\frac{{{\hbar ^2}}}{{12.855\,hc}}$$  g-cm²

  গ

  both equal to $$\frac{{{\hbar ^2}}}{{6.427\,hc}}$$  g-cm²

  ঘ

  zero and $$\frac{{{\hbar ^2}}}{{6.427\,hc}}$$  g-cm²
• The hyperfine splitting of the spectral lines of an atom is due to
  ক

  the coupling between the spins of two or more electrons

  খ

  the coupling between the spins and the orbital angular momentum of the electrons

  গ

  the coupling between the electron spin and the nuclear spin

  ঘ

  the effect of external electromagnetic fields
• The sodium doublet lines are due to transitions from ²p_3/2 and ²p_1/2 levels to ²s_1/2 level. On application of a weak magnetic field, the total number of allowed transitions becomes
  ক

  4

  খ

  6

  গ

  8

  ঘ

  10
• The degeneracies of the J-states arising from the ³p term with spin-orbit interaction are
  ক

  1, 3, 5

  খ

  1, 2, 3

  গ

  3, 5, 7

  ঘ

  2, 6, 10
• The allowed rotational energy levels of a rigid hetero-nuclear diatomic molecule are expressed as ε_J = BJ (J + 1), where B is the rotational constant and J is a rotational quantum number.<br>In a system of such diatomic molecules of reduced mass μ, some of the atoms of one element are replaced by a heavier isotope, such that the reduced mass is changed to 1.05μ. In the rotational spectrum of the system, the shift in the spectral line, corresponding to a transition J = 4 → J = 5, is
  ক

  0.475 B

  খ

  0.50 B

  গ

  0.95 B

  ঘ

  1.0 B
• The short wavelength, cut-off of the continuous X-ray spectrum from a nickel target is 0.0825 nm. The voltage required to.be applied to an X-ray tube is
  ক

  0.15 kV

  খ

  1.5 kV

  গ

  15 kV

  ঘ

  150 kV
• The vibrational spectrum of a molecule exhibits a strong line with P and R branches at a frequency $${\nu _1}$$ and a weaker line at a frequency $${\nu _2}$$ . The frequency $${\nu _3}$$ is not shown up. Its vibrational Raman spectrum shows a strongly polarized line at frequency $${\nu _3}$$ and no feature at $${\nu _1}$$ and $${\nu _2}$$ .<br>Which of the following statements is correct?
  ক

  The molecule could be linear

  খ

  The molecule lacks a centre of inversion

  গ

  $${\nu _1}$$ arises from a symmetric stretching mode

  ঘ

  $${\nu _3}$$ arises from a bending mode
• X-rays were produced using cobalt (Z = 27) as target. It was observed that the X-ray spectrum contained a strong K_α line of wavelength 0.1785 nm an a weak K_α line of wavelength 0.1930 nm. Then the weak K_α line is due to an impurity whose atomic number is
  ক

  25

  খ

  26

  গ

  28

  ঘ

  30
• For an electron in hydrogen atom, the states are characterized by the usual quantum numbers n, $$l$$, m_$$l$$. The electric dipole transition between any two states requires that
  ক

  Δ$$l$$ = 0, Δm_$$l$$ = 0, ±1

  খ

  Δ$$l$$ = ±1, Δm_$$l$$ = ±1, ±2

  গ

  Δ$$l$$ = ±1, Δm_$$l$$ = 0, ±1

  ঘ

  Δ$$l$$ = ±1, Δm_$$l$$ = 0, ±2
• The allowed states for He (2p²) configuration are
  ক

  ¹s₀, ³s₁, ¹p₁, ³p_{0, 1, 2}, ¹d₂ and ³d_{1, 2, 3}

  খ

  ¹s₀, ³p_{0, 1, 2} and ¹d₂

  গ

  ¹p₁ and ³p_{0, 1, 2}

  ঘ

  ¹s₀ and ¹p₁
• When the refractive index $$\mu $$ of the active medium changes by $${\Delta \mu }$$  in a laser resonator of length L, the change in the spectral spacing between the longitudinal modes of the laser is (c is the speed of light in free space)
  ক

  $$\frac{c}{{2\left( {\mu + \Delta \mu } \right)L}}$$

  খ

  $$\frac{c}{{2\Delta \mu L}}$$

  গ

  $$\frac{c}{{2L}}\frac{{\Delta \mu }}{{\mu \left( {\mu + \Delta \mu } \right)}}$$

  ঘ

  zero
• Five energy levels of a system including the ground state are shown below. Their lifetimes and the allowed electric dipole transitions are also marked.<br><img src="/images/question-image/engineering-physics/atomic-and-molecular-physics/1689658889-five-energy-levels-of-a-system.png" title="Atomic and Molecular Physics mcq question image" alt="Atomic and Molecular Physics mcq question image"><br>Which one of the following transitions is the most suitable for a Continuous Wave (CW) laser?
  ক

  1 → 0

  খ

  2 → 0

  গ

  4 → 2

  ঘ

  4 → 3
• The L_β line of X-rays emitted from an atom with principal quantum numbers n = 1, 2, 3, . . . . . . . ., arises from the transition
  ক

  n = 4 → n = 2

  খ

  n = 3 → n = 2

  গ

  n = 5 → n = 2

  ঘ

  n = 3 → n = 1
• If the equation of state for a gas with internal energy U is pV = $$\frac{1}{3}$$U, then the equation for an adiabatic process is
  ক

  pV^1/3 = constant

  খ

  pV^2/3 = constant

  গ

  pV^4/3 = constant

  ঘ

  pV^3/5 = constant
• The molecular spectra of two linear molecules O-C-O and O-C-S are recorded in the microwave region. Which one of the following statements is correct?
  ক

  Both the molecules would show absorption lines

  খ

  Both the molecules would not show absorption lines

  গ

  O-C-O would show absorption lines but not O-C-S

  ঘ

  O-C-S would show absorption lines but not O-C-O
• Match the typical spectra of stable molecules with the corresponding wave number range<br>
  ক

  <table class="table-style-1"> <tr> <td>P. Electronic spectra</td> <td>1. 10⁶ cm^-1 and above</td> </tr> <tr> <td>Q. Rotational spectra</td> <td>2. 10⁵ - 10⁶ cm^-1</td> </tr> <tr> <td>R. Molecular dissociation</td> <td>3. 10⁰ - 10² cm^-1</td> </tr></table> P-2, Q-1, R-3

  খ

  P-2, Q-3, R-1

  গ

  P-3, Q-2, R-1

  ঘ

  P-1, Q-2, R-3
• The rotational partition function for a diatomic molecule of moment of inertia $$I$$ at a temperature T is given by
  ক

  $$\frac{{I{k_B}T}}{{{\hbar ^2}}}$$

  খ

  $$\frac{{2I{k_B}T}}{{{\hbar ^2}}}$$

  গ

  $$\frac{{3I{k_B}T}}{{{\hbar ^2}}}$$

  ঘ

  $$\frac{{I{k_B}T}}{{2{\hbar ^2}}}$$
• A pure rotational Raman spectrum of a linear diatomic molecule is recorded using electromagnetic radiation of frequency $${\nu _e}$$ . The frequency of two consecutive Stokes lines are
  ক

  $${\nu _e}$$ - 10B, $${\nu _e}$$ - 14B

  খ

  $${\nu _e}$$ - 2B, $${\nu _e}$$ - 4B

  গ

  $${\nu _e}$$ + 10B, $${\nu _e}$$ + 14B

  ঘ

  $${\nu _e}$$ + 2B, $${\nu _e}$$ + 4B
• Two monochromatic waves having frequencies $$\omega $$ and $$\omega + \Delta \omega \left( {\Delta \omega \ll \omega } \right)$$    and corresponding wavelengths $$\lambda $$ and $$\lambda - \Delta \lambda \left( {\Delta \lambda \ll \lambda } \right)$$    of same polarization, travelling along X-axis are superimposed on each other. The phase velocity and group velocity of the resultant wave are respectively given by
  ক

  $$\frac{{\omega \lambda }}{{2\pi }},\,\frac{{\Delta \omega {\lambda ^2}}}{{2\pi \Delta \lambda }}$$

  খ

  $$\omega \lambda ,\,\frac{{\Delta \omega {\lambda ^2}}}{{\Delta \lambda }}$$

  গ

  $$\frac{{\omega \Delta \lambda }}{{2\pi }},\,\frac{{\Delta \omega \Delta \lambda }}{{2\pi }}$$

  ঘ

  $$\omega \Delta \lambda ,\,\omega \Delta \lambda $$
• Deuteron in its ground state has a total angular momentum J = 1 and a positive parity. The corresponding orbital angular momentum L and spin angular momentum S combinations are
  ক

  L = 0, S = 1 and L = 2, S = 0

  খ

  L = 0, S = 1 and L = 1, S = 1

  গ

  L = 0, S = 1 and L = 2, S = 1

  ঘ

  L = 1, S = 1 and L = 2, S = 1
• The last two terms of the electronic configuration of manganese (Mn) atom is 3d⁵ 4s². The term factor of Mn⁴⁺ ion is
  ক

  ⁴d_1/2

  খ

  ⁴f_3/2

  গ

  ³f_9/2

  ঘ

  ³d_7/2