Question

The figure below shows the infra-red rotation-vibration spectrum of nitrous oxide gas (N20). N20 드 2200 2210 2220 2230 2240 v/cm-1 From the information in the figure, and giving an outline of your working, calculate a value for the moment of inertia of this linear molecule for its active rotational mode.

Answer 1

In the question, the IR spectra of the molecule N₂O is given

We know that in case of vibrational spectroscopy we have

$\bar{\nu } = \bar{\nu _{0}} + 2 Bm$

where $\bar{\nu _{0}}$ is the central wave number (m= 0 case)

B - rotational constant

We know that for P branch lines, m has negative values as -1, -2 ,-3 etc and for R branch lines m has positive  values as 1, 2 ,3 etc. Thus the lines in the spectra will be P1, P2,P3​​​​​​​,P4​​ etc and R₀, R₁, R₂ etc.

from spectra, we have values of P branch lines as 2223 cm^-1, 2222 cm^-1, 2221 cm^-1, 2220 cm^-1, 2219 cm^-1.

from spectra, we have values of P branch lines as 2225 cm^-1, 2226 cm^-1, 2227 cm^-1, 2228 cm^-1, 2229 cm^-1.

Pl + P2 + Ps + P4 P5 + Ro + R1 + R2+ R3 + R4 2219 + 2220 + 2221 2222 + 2223+2225 +2226 2227 +2228+2229 Vo 10 10 2224cm
similarly we can get,
Ro- P 2225 - 2223 B= -1

again we know that

0.5cm-1

moment of inertia ​​​​​​​

6.626 × 10-34 0.5x3x1010kgTn2 = 5.595 × 10-46kgm" 8π2Be = 8r2