Molecular Spectra - Atomic and Molecular Physics - Physics Previous Year Questions

1

2007 · Physics · Atomic and Molecular Physics · Molecular Spectra

Physics (PH) 2007

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

A

\(0.475 B \)

B

\(0.50 B \)

C

\(0.95 B \)

D

\(1.0 B \)

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2

2007 · Physics · Atomic and Molecular Physics · Molecular Spectra

Physics (PH) 2007

The number of fundamental vibrational modes of \( CO_2 \) molecule is

A

four : 2 are Raman active and 2 are infrared active.

B

four : 1 is Raman active and 3 are infrared active.

C

three: 1 is Raman active and 2 are infrared active.

D

three: 2 are Raman active and 1 is infrared active.

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3

2007 · Physics · Atomic and Molecular Physics · Molecular Spectra

Physics (PH) 2007

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

A

\(0.475 B \)

B

\(0.50 B \)

C

\(0.95 B \)

D

\(1.0 B \)

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4

2007 · Physics · Atomic and Molecular Physics · Molecular Spectra

Physics (PH) 2007

The solid phase of an element follows van der Waals bonding with inter-atomic potential \( V(r) = -\frac{P}{r^6} + \frac{Q}{r^{12}} \), where \( P \) and \( Q \) are constants. The bond length can be expressed as

A

\(\left(\frac{2Q}{P}\right)^{-6} \)

B

\(\left(\frac{Q}{P}\right)^{-6} \)

C

\(\left(\frac{P}{2Q}\right)^{-6} \)

D

\(\left(\frac{P}{Q}\right)^{-6} \)

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5

2008 · Physics · Atomic and Molecular Physics · Molecular Spectra

Physics (PH) 2008

Three consecutive absorption lines at \(64.275 \text{ cm}^{-1}, 77.130 \text{ cm}^{-1}\) and \(89.985 \text{ cm}^{-1}\) 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)

A

both equal to \(\frac{h^2}{12.855 hc} \text{ gm cm}^2\)

B

zero and \(\frac{h^2}{12.855 hc} \text{ gm cm}^2\)

C

both equal to \(\frac{h^2}{6.427 hc} \text{ gm cm}^2\)

D

zero and \(\frac{h^2}{6.427 hc} \text{ gm cm}^2\)

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6

2008 · Physics · Atomic and Molecular Physics · Molecular Spectra

Physics (PH) 2008

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

A

\(\nu_e - 10B, \quad \nu_e - 14B\)

B

\(\nu_e - 2B, \quad \nu_e - 4B\)

C

\(\nu_e + 10B, \quad \nu_e + 14B\)

D

\(\nu_e + 2B, \quad \nu_e + 4B\)

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7

2008 · Physics · Atomic and Molecular Physics · Molecular Spectra

Physics (PH) 2008

Which one of the following statement is INCORRECT in vibrational spectroscopy with anharmonicity?

A

The selection rule for vibrational spectroscopy is \(\Delta v = \pm 1, \pm 2, ...\)

B

Anharmonicity leads to multiple absorption lines.

C

The intensities of hot band lines are stronger than the fundamental absorption.

D

The frequencies of hot band lines are smaller than the fundamental absorption.

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8

2008 · Physics · Atomic and Molecular Physics · Molecular Spectra

Physics (PH) 2008

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 statement is correct?

A

Both the molecules would show absorption lines.

B

Both the molecules would not show absorption lines.

C

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

D

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

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9

2009 · Physics · Atomic and Molecular Physics · Molecular Spectra

Physics (PH) 2009

The separation between the first Stokes and corresponding anti-Stokes lines of the rotational Raman spectrum in terms of the rotational constant, B is

A

2B

B

4B

C

6B

D

12B

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10

2009 · Physics · Atomic and Molecular Physics · Molecular Spectra

Physics (PH) 2009

In a diatomic molecule, the internuclear separation of the ground and first excited electronic state are the same as shown in the figure. If the molecule is initially in the lowest vibrational state of the ground state, then the absorption spectrum will appear as

A

A graph of intensity vs cm^-1 with a series of sharp peaks of increasing spacing.

B

A graph of intensity vs cm^-1 with a series of sharp peaks of equal spacing.

C

A graph of intensity vs cm^-1 with a broad continuum band and a sharp peak.

D

A graph of intensity vs cm^-1 with a series of sharp peaks of varying intensity.

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11

2010 · Physics · Atomic and Molecular Physics · Molecular Spectra

Physics (PH) 2010

The three principal moments of inertia of a methanol (CH3OH) molecule have the property \( I_x = I_y = I \) and \( I_z \neq I \). The rotational energy eigenvalues are

A

\(\frac{\hbar^2}{2I} l(l+1) + \frac{\hbar^2 m_l^2}{2} \left( \frac{1}{I_z} - \frac{1}{I} \right) \)

B

\(\frac{\hbar^2}{2I} l(l+1) \)

C

\(\frac{\hbar^2 m_l^2}{2} \left( \frac{1}{I_z} - \frac{1}{I} \right) \)

D

\(\frac{\hbar^2}{2I} l(l+1) + \frac{\hbar^2 m_l^2}{2} \left( \frac{1}{I_z} + \frac{1}{I} \right) \)

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12

2010 · Physics · Atomic and Molecular Physics · Molecular Spectra

Physics (PH) 2010

Match the typical spectra of stable molecules with the corresponding wave-number range
1. Electronic spectra
2. Rotational spectra
3. Molecular dissociation

A

1 – ii, 2 – i, 3 – iii

B

1 – ii, 2 – iii, 3 – i

C

1 – iii, 2 – ii, 3 – i

D

1 – i, 2 – ii, 3 – iii

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13

2011 · Physics · Atomic and Molecular Physics · Molecular Spectra

Physics (PH) 2011

The far infrared rotational absorption spectrum of a diatomic molecule shows equidistant lines with spacing \(20\ \text{cm}^{-1}\). The position of the first Stokes line in the rotational Raman spectrum of this molecule is

A

\(20\ \text{cm}^{-1}\)

B

\(40\ \text{cm}^{-1}\)

C

\(60\ \text{cm}^{-1}\)

D

\(120\ \text{cm}^{-1}\)

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14

2012 · Physics · Atomic and Molecular Physics · Molecular Spectra

Physics (PH) 2012

The first Stokes line of a rotational Raman spectrum is observed at 12.96 cm^{-1}. Considering the rigid rotor approximation, the rotational constant is given by

A

6.48 cm^{-1}

B

3.24 cm^{-1}

C

2.16 cm^{-1}

D

1.62 cm^{-1}

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15

2012 · Physics · Atomic and Molecular Physics · Molecular Spectra

Physics (PH) 2012

The equilibrium vibration frequency for an oscillator is observed at 2990 cm^-1. The ratio of the frequencies corresponding to the first and the fundamental spectral lines is 1.96. Considering the oscillator to be anharmonic, the anharmonicity constant is

A

0.005

B

0.02

C

0.05

D

0.1

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16

2013 · Physics · Atomic and Molecular Physics · Molecular Spectra

Physics (PH) 2013

The spacing between vibrational energy levels in CO molecule is found to be \( 8.44 \times 10^{-2} \) eV. Given that the reduced mass of CO is \( 1.14 \times 10^{-26} \) kg, Planck’s constant is \( 6.626 \times 10^{-34} \) Js and \( 1eV = 1.6 \times 10^{-19} \) J. The force constant of the bond in CO molecule is

A

1.87 N/m

B

18.7 N/m

C

187 N/m

D

1870 N/m

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17

2014 · Physics · Atomic and Molecular Physics · Molecular Spectra

Physics (PH) 2014

The moment of inertia of a rigid diatomic molecule \(A\) is 6 times that of another rigid diatomic molecule \(B\). If the rotational energies of the two molecules are equal, then the corresponding values of the rotational quantum numbers \(J_A\) and \(J_B\) are

A

\(J_A = 2, J_B = 1\)

B

\(J_A = 3, J_B = 1\)

C

\(J_A = 5, J_B = 0\)

D

\(J_A = 6, J_B = 1\)

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18

2015 · Physics · Atomic and Molecular Physics · Molecular Spectra

Physics (PH) 2015

The excitation wavelength of laser in a Raman effect experiment is 546 nm. If the Stokes' line is observed at 552 nm, then the wavenumber of the anti-Stokes' line (in cm⁻¹) is __________

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19

2015 · Physics · Atomic and Molecular Physics · Molecular Spectra

Physics (PH) 2015

In a rigid-rotator of mass \(M\), if the energy of the first excited state is \(1\ meV\), then the fourth excited state energy (in \(meV\)) is __________

A

B

C

D

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20

2016 · Physics · Atomic and Molecular Physics · Molecular Spectra

Physics (PH) 2016

The molecule \(^{17}O_2\) is

A

Raman active but not NMR (nuclear magnetic resonance) active.

B

Infrared active and Raman active but not NMR active.

C

Raman active and NMR active.

D

Only NMR active.

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