This set of Physical Chemistry Multiple Choice Questions & Answers (MCQs) focuses on “Symmetry Elements and Symmetry Operations”.

1. What is the name given to a plane in which all the atoms are reflected across the plane which perpendicular to its principal axis and the molecule having unchanged in configuration?

a) Vertical reflection plane

b) Diagonal reflection plane

c) Horizontal reflection plane

d) Dihedral reflection plane

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Explanation: Horizontal reflection plane is the plane which passes through the origin and perpendicular to the axis with the highest symmetry. Vertical reflection plane is the plane which passes through the origin and the axis with the highest symmetry.

2. What kind of symmetry planes does the molecule of CH_{3}Cl has?

a) Three of vertical symmetry planes

b) One of horizontal symmetry plane

c) One of vertical symmetry plane

d) Two of dihedral symmetry planes

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Explanation: CH

_{3}Cl belongs to the C

_{3v}point group. It has the symmetry element E, a C

_{3}axis, and three σ

_{v}planes. Thus, it has three vertical planes of symmetry. In drawing a vertical plane that includes Cl-C bond and the closest H, the left hand side and the right hand side mirror images of each other are visible.

3. How many types of symmetry elements are there?

a) Four

b) Five

c) Two

d) Three

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Explanation: There are three types of symmetry operations- rotation, reflection and inversion. A symmetry element is geometrical entity about which a symmetry operation is performed. A symmetry element can be a point, axis, or plane.

4. A symmetry element is a point of reference about which symmetry operations can take place.

a) False

b) True

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Explanation: The given statement is true because symmetry element is a line, a plane or a point in or through an object, about which a rotation or reflection leaves the object in an orientation indistinguishable from the original.

5. Which of the following symmetry element is denoted by S_{n}?

a) Improper rotation

b) Rotational symmetry

c) Inversion

d) Identity

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Explanation: An improper rotation is the composition of a rotation about an axis and a reflection in a plane perpendicular to that axis. Its group is denoted by S

_{n}?. A group of proper rotations is denoted by C

_{n}?, where n is the order of rotation.

6. Which of the following are the inverted position vectors of a point?

a) (-x, y, z)

b) (-x, -y, -z)

c) (x, y, z)

d) (x, y, -z)

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Explanation: In the inversion operation for 3D coordinates, the inversion center is the origin (0, 0, 0). When an object is inverted, the position vector of a point in an object (x, y, z), is inverted to (-x, -y, -z). Therefore, (-x, -y, -z) are the inverted position vectors of a point.

7. Which of the following symmetry element is found in all objects?

a) An inversion center

b) A group of rotational symmetry

c) Mirror planes

d) Identity

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Explanation: The identity symmetry element is found in all objects and is denoted by E. It corresponds to an operation of doing nothing to the object. The symmetry of a figure is a basic rigid motion that maps the figure back onto itself.

8. Which of the following symmetry element is denoted by C_{n}?

a) Mirror planes

b) A group of proper rotational symmetry

c) An inversion center

d) Identity

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Explanation: A group of proper rotations is denoted as C

_{n}?, where n is the order of rotation. Rotational symmetry, also known as radial symmetry, is represented by an axis about which the object rotates in its corresponding symmetry operation.

9. Which of the following symmetry element is denoted by i?

a) Identity

b) Rotational symmetry

c) An inversion

d) Mirror planes

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Explanation: Inversion is denoted by i. The center point of the object is called the inversion center. For the inversion operation for 3D coordinates, the inversion center is the origin that is (0, 0, 0). The inversion center is an important characteristic of the object.

10. Which of the following is denoted by σ in symmetry elements?

a) Mirror planes

b) Rotational symmetry

c) Identity

d) Inversion

View Answer

Explanation: Mirror planes are denoted by σ. In particular, a vertical mirror plane is denoted by σ

_{v}. A plane of reflection through which an identical copy of the original molecule is generated is called the mirror plane.

**Sanfoundry Global Education & Learning Series – Physical Chemistry.**

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