Five lines of the fundamental band ( ) are measured at , , , ,

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

Deriving the Spectrum, Ch Diatomic rotation-vibration spectra and nuclear spin statistics

Problem

Five lines of the

\mathrm{H}^{35}\mathrm{Cl}

fundamental band (

v=0\to1

) are measured at

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

P(2) = 2843.61\,\mathrm{cm^{-1}}

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

R(1) = 2925.92\,\mathrm{cm^{-1}}

R(2) = 2944.97\,\mathrm{cm^{-1}}

. Someone argues: "Adjacent lines of the

R

branch,

R(1)

and

R(2)

, are separated by

2944.97 - 2925.92 = 19.05\,\mathrm{cm^{-1}}

. Since the spacing between adjacent rotational lines is always

2B

, the rotational constant is

B = 19.05/2 = 9.53\,\mathrm{cm^{-1}}

." ((a)) Explain what is wrong with this reasoning. ((b)) Use the method of combination differences on the given lines to find the correct values of

B_0

and

B_1

(in

\mathrm{cm^{-1}}

). ((c)) Hence find

\alpha_e

B_e

and the equilibrium bond length

R_e

, taking atomic masses

m_{\rm H} = 1.00783\,\mathrm{u}

and

m_{\rm Cl} = 34.96885\,\mathrm{u}

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