Group Theory - Physical Chemistry - Chemistry Previous Year Questions

1

2008 · Chemistry · Physical Chemistry · Group Theory

Chemistry (CY) 2008

The T_d point group has 24 elements and 5 classes. Given that it has two 3-dimensional irreducible representations, the number of one dimensional irreducible representations is

A

1

B

6

C

2

D

3

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2

2009 · Chemistry · Physical Chemistry · Group Theory

Chemistry (CY) 2009

The reducible representation corresponding to the three translational degrees of freedom, Γ_tr, is

A

3, 1, 1, 1

B

3, −1, 1, 1

C

3, −1, −1, −1

D

3, 1, −1, −1

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3

2009 · Chemistry · Physical Chemistry · Group Theory

Chemistry (CY) 2009

The asymmetric stretching mode of the H₂O is shown below. The molecular plane is yz and the symmetry axis of H₂O is z.

This vibration transforms as the irreducible representation

A

A₁

B

B₁

C

A₂

D

B₂

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4

2011 · Chemistry · Physical Chemistry · Group Theory

Chemistry (CY) 2011

The point group symmetry of the given planar shape is

A

D_2h

B

C₂

C

C_2h

D

C_2v

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5

2012 · Chemistry · Physical Chemistry · Group Theory

Chemistry (CY) 2012

Symmetry operations of the four C₂ axes perpendicular to the principal axis belong to the same class in the point group(s)

A

D₄

B

D_3d

C

D_4h

D

D_4h and D_3d

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6

2013 · Chemistry · Physical Chemistry · Group Theory

Chemistry (CY) 2013

The point group symmetry of $CH_2=C=CH_2$ is

A

D_{2h}

B

C_{2h}

C

C_{2v}

D

D_{2d}

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7

2023 · Chemistry · Physical Chemistry · Group Theory

Chemistry (CY) 2023

Point group of naphthalene (C10H8) is

A

D_2d

B

D_2h

C

D_3d

D

D_3h

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8

2024 · Chemistry · Physical Chemistry · Group Theory

Chemistry (CY) 2024

The order and the number of classes present in a group with the irreducible representations A1, A2, B1, B2, E1, and E2, are, respectively,

A

6 and 6

B

12 and 6

C

6 and 3

D

12 and 3

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9

2024 · Chemistry · Physical Chemistry · Group Theory

Chemistry (CY) 2024

Among the following, the correct statement(s) is (are):

A

C₂ symmetry element is present in H₂O and H₂O₂ but NOT in PCl₅.

B

both C₂ and C₃ symmetry elements are present in CCl₄ and SF₆.

C

one \(\sigma_h\) and three \(\sigma_d\) symmetry elements are present in benzene.

D

\(\sigma_v\) symmetry element is present in NH₃ but NOT in BF₃.

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10

2025 · Chemistry · Physical Chemistry · Group Theory

Chemistry (CY) 2025

The symmetry element that does NOT belong to \(C_{4v}\) point group is

A

\(C_4\)

B

\(C_2\)

C

\(i\)

D

\(\sigma_v\)

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11

2007 · Chemistry · Physical Chemistry · Group Theory

Chemistry (CY) 2007

The S₂ operation on a molecule with the axis of rotation as the z axis, moves a nucleus at (x, y, z) to

A

(−x, −y, z)

B

(x, −y, −z)

C

(−x, y, −z)

D

(−x, −y, −z)

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12

2007 · Chemistry · Physical Chemistry · Group Theory

Chemistry (CY) 2007

The number of distinct symmetry operations that can be performed on the molecule is

A

2

B

4

C

6

D

8

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13

2007 · Chemistry · Physical Chemistry · Group Theory

Chemistry (CY) 2007

The number of irreducible representations of the point group of the molecule is

A

1

B

2

C

3

D

4

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14

2007 · Chemistry · Physical Chemistry · Group Theory

Chemistry (CY) 2007

When two H atoms of the above molecule are also replaced by F atoms, the point group of the resultant molecule will be

A

C_i

B

C_2h

C

C_2v

D

D_2h

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15

2018 · Chemistry · Physical Chemistry · Group Theory

Chemistry (CY) 2018

A set of 4 parallel lines intersect with another set of 5 parallel lines. How many parallelograms are formed?

A

20

B

48

C

60

D

72

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16

2021 · Chemistry · Physical Chemistry · Group Theory

Chemistry (CY) 2021

The characters of E, C₂, σ_v, and σ'_v symmetry operations, in this order, for valid irreducible representation(s) of the C_2v point group is/are:

A

1, 1, 1, 1

B

–1, 1, 1, –1

C

1, –1, 1, –1

D

1, –1, –1, –1

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17

2021 · Chemistry · Physical Chemistry · Group Theory

Chemistry (CY) 2021

The normal mode(s) of vibration of H₂O is/are:

A

B

C

D

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18

2022 · Chemistry · Physical Chemistry · Group Theory

Chemistry (CY) 2022

A point originally at (1, 3, 5) was subjected to a symmetry operation (Ô₁) that shifted the point to (–1, –3, 5). Subsequently, the point at (–1, –3, 5) was subjected to another symmetry operation (Ô₂) that shifted this point to (–1, –3, –5). The symmetry operators Ô₁ and Ô₂ are, respectively,

A

Ĉ₂(x) and σ̂(xy)

B

Ĉ₂(z) and σ̂(xy)

C

σ̂(xy) and Ĉ₂(z)

D

Ŝ₁ and Ŝ₂

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19

2022 · Chemistry · Physical Chemistry · Group Theory

Chemistry (CY) 2022

For three operators \(\hat{A}\), \(\hat{B}\), and \(\hat{C}\), \(\left[\hat{A},[\hat{B},\hat{C}]\right] + \left[\hat{B},[\hat{C},\hat{A}]\right] =\)

A

\(\left[\hat{C},[\hat{A},\hat{B}]\right]\)

B

\(\left[\hat{C},[\hat{B},\hat{A}]\right]\)

C

\(\left[[\hat{B},\hat{A}],\hat{C}\right]\)

D

\(\left[[\hat{A},\hat{B}],\hat{C}\right]\)

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20

2026 · Chemistry · Physical Chemistry · Group Theory

Chemistry (CY) 2026

The point group of CH2=C=CH2 is

A

\(D_{2h}\)

B

\(C_{2h}\)

C

\(C_{2v}\)

D

\(D_{2d}\)

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