The two lines nearest the centre of the fundamental band of are measured at and…

PHYSICS · Multi-part · Fermi University Physics · Atomic, Molecular & Optical Physics · Molecular structure and spectra · Molecular structure and spectra

Reading the Spectrum, Ch Two nuclei on one curve: rotation, vibration and the spectrum of a diatomic molecule

Problem

The two lines nearest the centre of the fundamental band of

\mathrm{H^{35}Cl}

are measured at

\mathrm{P}(1) = 2865.10\,\mathrm{cm^{-1}}

and

\mathrm{R}(0) = 2906.25\,\mathrm{cm^{-1}}

(HITRAN2016). Each has a weaker partner from

\mathrm{H^{37}Cl}

just below it. Take

\mu = 0.97959\,\mathrm u

for

\mathrm{H^{35}Cl}

and

0.98108\,\mathrm u

for

\mathrm{H^{37}Cl}

, and

\omega_ex_e = 52.8\,\mathrm{cm^{-1}}

from the overtone. ((a)) Treating the band with one rotational constant, find

\tilde\nu_0

and

B

from the two lines. ((b)) Find the bond length this

B

implies. It comes out longer than the

R_0 = 128.4\,\mathrm{pm}

found from

B_0 = 10.44\,\mathrm{cm^{-1}}

; say why. ((c)) Find

\omega_e

from

\tilde\nu_0 = \omega_e - 2\omega_ex_e

, and the force constant

k

. ((d)) Predict where the

\mathrm{H^{37}Cl}

partner of R(0) falls, scaling

\omega_e

\mu^{-1/2}

and both

\omega_ex_e

and

B

\mu^{-1}

, and find how far apart the pair is. ((e)) A grating with

150

grooves per millimetre is used in first order. How many grooves must be illuminated to separate the pair, and how wide a strip of grating is that?

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