Complete Question
Find the ratio of intensities in 4 different sets of red to violet spectral satellites in Raman scattering spectra of CCl4 molecules at T=27C temperature if corresponding resonant infrared frequencies (equivalent to frequencies of nuclei vibrations) of CCl4 molecule are 217, 315, 457 and 774 cm-1 . (Note: Wavenumber N in cm-1 is defined as [tex]N=1/\lambda\ cm^{-1}[/tex])
Answer:
The ratio of intensities is [tex]I_1 : I_2 : I_3 : I_4 = 217 : 315 : 457 : 774[/tex]
Explanation:
From the question we are told that
The number of sets of satellite is [tex]n = 4[/tex]
The temperature is [tex]T = 27 ^oC[/tex]
The resonant infrared frequencies are [tex]f_1 = 217 cm^{-1}[/tex]
[tex]f_2 = 315 cm^{-1}[/tex]
[tex]f_3 = 457 cm^{-1}[/tex]
[tex]f_4 = 774 cm^{-1}[/tex]
From the question we see that the wave number also has a unit of[tex]cm^{-1}[/tex] hence the value of the wave numbers of the molecule are
[tex]N_1 = 217 cm^{-1}[/tex]
[tex]N_2 = 315 cm^{-1}[/tex]
[tex]N_3 = 457 cm^{-1}[/tex]
[tex]N_4 = 774 cm^{-1}[/tex]
Generally intensity is mathematically represented as
[tex]I = \frac{nhc}{A \lambda }[/tex]
Here we see that I varies inversely with wavelength i,.e
[tex]I \ \ \alpha \ \ \frac{1}{\lambda }[/tex]
From the question we are told that the wave number is mathematically represented as
[tex]N = \frac{1}{\lambda }[/tex]
Therefore
[tex]I \ \ \alpha \ \ N[/tex]
This implies that the ratio of intensity in first set to that of second set to that of third set to that of fourth set is equal to the ratio of the wavenumber in the first set to that of the second set to that of third set to that of fourth
This is mathematically represented as
[tex]I_1 : I_2 : I_3 : I_4 = N_1 : N_2 : N_3 : N_4[/tex]
Substituting values
[tex]I_1 : I_2 : I_3 : I_4 = 217 : 315 : 457 : 774[/tex]
