Question

The following Raman data were obtained for ${\mathrm{CHCl}}_3$with the polarizer of the spectrometer set (1) parallel to the plane of polarization of the laser and (2) at $90°$to the plane of the source.

Calculate the depolarization ratio and indicate which Raman lines are polarized.

Short answer

(a) The depolarization ratio at wave number $760{\mathrm{cm}}^{-1}$is $0.77$and the Raman lines are depolarized.

(b) The depolarization ratio at wave number $660{\mathrm{cm}}^{-1}$is $0.012$and the Raman lines are polarized.

(c) The depolarization ratio at wave number $357{\mathrm{cm}}^{-1}$is $0.075$and the Raman lines are polarized.

(d) The depolarization ratio at wave number $258{\mathrm{cm}}^{-1}$is$0.76$ and the Raman lines are depolarized.

Step-by-step solution

Part (a) Step 1. Given information

The wavenumber, $∆\overline{v}=760{\mathrm{cm}}^{-1}$

The parallel polarizer,$I_{\parallel }=0.60$

The perpendicular polarizer, $I_{\perp }=0.46$

Part (a) Step 2. Calculate the depolarization ratio and indicate its polarizability

The expression for the depolarization ratio is as follows:

$p=\frac{I_{\perp }}{I_{\parallel }}$

Substitute the values in the above equation as follows:

$$\begin{gathered} p=\frac{0.46}{0.60} \\ =0.77 \end{gathered}$$

The depolarization ratio at wave number $760{\mathrm{cm}}^{-1}$is $0.77$.

The value of depolarization ratio is $0.77$, which is maximum hence the Raman lines are depolarized. Thus, the Raman lines are depolarized.

Part (b) Step 1. Given information 

The wavenumber, $∆\overline{v}=660{\mathrm{cm}}^{-1}$

The parallels polarizer, $I_{\parallel }=8.4$

The perpendicular polarizer, $I_{\perp }=0.1$

Part (b) Step 2. Calculate the depolarization ratio and indicate its polarizability 

The expression for the depolarization ratio is as follows:

$p=\frac{I_{\perp }}{I_{\parallel }}$

Substitute the values in the above equation as follows:

$$\begin{gathered} p=\frac{0.1}{8.4} \\ =0.012 \end{gathered}$$

The depolarization ratio at wave number $660{\mathrm{cm}}^{-1}$is $0.012$.

The value of depolarization ratio is $0.012$, which is minimal value hence the Raman lines are polarized. Thus, the Raman lines are polarized.

Part (c) Step 1. Given information

The wavenumber,$∆\overline{v}=357{\mathrm{cm}}^{-1}$

The parallel polarizer,$I_{\parallel }=7.9$

The perpendicular polarizer,$I_{\perp }=0.6$

Part (c) Step 2. Calculate the depolarization ratio and indicate its polarizability 

The expression for the depolarization ratio is as follows:

$p=\frac{I_{\perp }}{I_{\parallel }}$

Substitute the values in the above equation as follows:

$$\begin{gathered} p=\frac{0.6}{7.9} \\ =0.075 \end{gathered}$$

The depolarization ratio at wave number $357{\mathrm{cm}}^{-1}$is $0.075$.

The value of depolarization ratio is $0.075$, which is minimal value hence the Raman lines are polarized. Thus, the Raman lines are polarized.

Part (d) Step 1. Given information 

The wavenumber,$∆\overline{v}=258{\mathrm{cm}}^{-1}$

The parallel polarizer,$I_{\parallel }=4.2$

The perpendicular polarizer,$I_{\perp }=3.2$

Part (d) Step 2. Calculate the depolarization ratio and indicate its polarizability 

The expression for the depolarization ratio is as follows:

$p=\frac{I_{\perp }}{I_{\parallel }}$

Substitute the values in the above equation as follows:

$$\begin{gathered} p=\frac{3.2}{4.2} \\ =0.76 \end{gathered}$$

The depolarization ratio at wave number localid="1645511487432" $258{\mathrm{cm}}^{-1}$is localid="1645511495538" $0.76$.

The value of depolarization ratio is localid="1645511546383" $0.76$, which is maximum value hence the Raman lines are depolarized. Thus, the Raman lines are depolarized.