Problem: Determine the point group of the molecule CCl4.
Solution:
Step 1: Identify the molecule's shape and geometry. The molecule CCl4 has a tetrahedral geometry.
Step 2: Determine the symmetry elements. The molecule CCl4 has the following symmetry elements:
Four C3 axes passing through the carbon atom and the center of opposite C-Cl bonds.
Three planes of symmetry passing through the carbon atom and the midpoint of opposite C-Cl bonds.
A center of inversion at the center of the molecule.
Step 3: Determine the point group. To determine the point group of the molecule CCl4, we need to compare its symmetry elements with the symmetry elements of known point groups. By comparing the symmetry elements, we find that the molecule CCl4 belongs to the Td point group.
Step 4: Apply group theory to solve the problem. The character table for the Td point group is as follows:
E 8C3 3C2 6S4 6σd
1 1 1 1 1
4 -1 1 0 -1
2 0 -1 1 2
4 1 1 0 -1
2 0 -1 -1 2
To determine the irreducible representations of the molecule CCl4, we need to apply each symmetry operation to the molecule and determine how the molecule is transformed. The molecule CCl4 has the following irreducible representations:
A1: The identity operation leaves the molecule unchanged.
T1: The three C3 axes and the center of inversion transform the molecule into three equivalent forms.
T2: The three planes of symmetry transform the molecule into two equivalent forms.
A2: The product of any two C2 axes in perpendicular planes transforms the molecule into its mirror image.
Step 5: Apply the selection rules. The selection rules determine which transitions or reactions are allowed or forbidden based on the symmetry of the initial and final states and the symmetry of the operator involved in the transition. For example, the transition moment between two electronic states is only allowed if the product of the irreducible representations of the two states and the operator involved in the transition is non-zero.
Step 6: Solve the problem. Based on the irreducible representations of the molecule CCl4, we can predict the spectroscopic properties and chemical reactivity of the molecule. For example, we can predict that the molecule CCl4 has no dipole moment because the A1 irreducible representation is the only one that has a non-zero value for the x, y, and z coordinates. This means that the transition between the ground state and the excited state with the same symmetry will not be observed in the electronic spectra of CCl4.
I hope this example helps you understand the steps involved in solving point group problems in the CSIR NET exam. Remember to practice regularly and use reliable resources to improve your understanding of group theory and symmetry operations.
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