91影视

The number of waves that are present in the unit distance is termed a wave number. The wave number and wavelength are related as:

$\mathbf{wave}鈥�\mathbf{number}\mathbf{=}\frac{\mathbf{1}}{\mathbf{wave}鈥�\mathbf{length}}$

The IR-absorption frequency is proportional to $\sqrt{\frac{k}{m}}$,where k is the force constant and m is the mass of the lighter atom.

Given IR-absorption frequency for C-H bond is$3000鈥�c{m}^{-1}$ .

The mass of D-atom is 2 amu.

The mass of H-atom is 1 amu.

The IR-absorption frequency for C-D bond can be calculated as shown:

$$\begin{gathered} \frac{{谓}_{C-H}}{{谓}_{C-D}}=\sqrt{\frac{k}{1鈥�amu}脳\frac{2鈥�amu}{k}} \\ \frac{{谓}_{C-H}}{{谓}_{C-D}}=\sqrt{2} \\ {谓}_{C-D}=\frac{{谓}_{C-H}}{\sqrt{2}} \\ {谓}_{C-D}=\frac{3000鈥�c{m}^{-1}}{\sqrt{2}} \end{gathered}$$

On simplification,

${谓}_{C-D}=2121鈥�c{m}^{-1}$

Hence, the IR-absorption frequency of C-D bond is $2121鈥�c{m}^{-1}$.

The C-D bond stretching frequency around$2100鈥�c{m}^{-1}$ matches with the stretching frequency of the$C鈮�C$ . So, if$CDC{l}_3$ is present as an impurity, then it interrupts with the stretching frequencies of the $C鈮�C$if they are present in the given sample