The observed IR spectrum for BCl₃ exhibits three bands at 995, 480 and 244 cm^-1, while the Raman bands are observed at 995, 471 and 244cm^-1. Given that for BCl₃,

the frequency of A₁^'​mode in cm^-1is:

Correct option is B

Criterion of feasibility of a transition

Symmetry selection rules for Infrared Spectra

For the fundamental transition in the ith normal mode of vibration,

​where Ψ₀ is the vibrational ground wave function and Ψ₁, is the vibrational first excited wave function. It is known that
(i) The vibrational ground wave function is totally symmetric.
(ii) The symmetry properties of the component of the dipole moment are the same as those of a translational vector along the same axis.
(iii) The symmetric properties of the first excited vibrational wave function are the same as those of irreducible representation of the normal mode of vibration.
In order that the direct product of

​belongs to the totally symmetric representation, both

​should belong the same representation.

Thus the essential criterion for observing fundamental transition in the infrared spectroscopy is

A fundamental transition will be infrared active if the normal mode which is excited belongs to the same representation as any one or several of the Cartesian coordinates.

Symmetry selection rules for Raman Spectra

The symmetry selection rule for Raman spectra is derived from the integral

A fundamental transition will be Raman active if the normal mode involved belongs to the same irreducible representation as one or more of the components of the polarizability tensor of the molecule.

E' and A₂^" are IR active.

E^' and A₁^'are Raman active.

Both bands at 995 and 244 cm^-1 are observed in the IR and Raman spectrum of the BCl₃ molecule. As only the E' mode is common between the IR and Raman spectrum of the BCl₃ molecule, the frequency of E' mode is 995 and 244 cm^-1. Thus, the remaining A₁^' mode in Raman spectrum has a frequency of 471 cm^-1.