A microwave-plasma source generates a transient diatomic radical AB

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

Deriving the Spectrum, Ch Electronic spectra of diatomic molecules

Problem

A microwave-plasma source generates a transient diatomic radical AB, and a diagnostics team records its electronic, photoelectron and Raman spectra in the same run. Treat every electronic band origin as a pure vibronic term

\nu_{v'v''}=T_e+G'(v')-G''(v'')

with

G(v)=\omega_e(v+\tfrac12)-\omega_ex_e(v+\tfrac12)^2

, ignore rotational structure throughout, and use

c=2.998\times10^{10}\,\mathrm{cm\,s^{-1}}

k_{\rm B}=8.617\times10^{-5}\,\mathrm{eV\,K^{-1}}

and

1\,\mathrm{cm^{-1}}=1.23984\times10^{-4}\,\mathrm{eV}

. ((a)) Nine band origins of a

B

X

system of AB, in

\mathrm{cm^{-1}}

, are tabulated below by upper level

v'

(rows) and lower level

v''

(columns): Data (band origins in

\mathrm{cm^{-1}}

for lower level

v''=0

1

2

): for

v'=0

29874.25

29034.25

28204.25

; for

v'=1

30458.25

29618.25

28788.25

; for

v'=2

31026.25

30186.25

29356.25

. Use row and column differences in this Deslandres table to obtain

\omega_e'

\omega_e'x_e'

(upper state) and

\omega_e''

\omega_e''x_e''

(lower state). ((b)) Bands with

v'\le5

are Doppler-limited, of width

0.05\,\mathrm{cm^{-1}}

, with full fluorescence. From

v'=6

upward every band suddenly broadens to

2.10\,\mathrm{cm^{-1}}

and its fluorescence quantum yield falls to

1.0\%

, although

v'=6

lies far below the dissociation limit of the

B

state. Name the mechanism responsible for this onset, and find the radiative rate constant

k_{\rm rad}

and the extra non-radiative rate constant that switches on above

v'=6

. ((c)) A He I photoelectron spectrum of AB (

h\nu=21.2\,\mathrm{eV}

) shows two bands. The first has its

v'=0

line at an ionisation energy of

10.5\,\mathrm{eV}

and only two further lines beyond it. The second has its

v'=0

line at

13.0\,\mathrm{eV}

and a long progression of at least eight further lines. Find the kinetic energy of the photoelectrons in the

v'=0

line of each band, and state which of the two orbitals removed is the more strongly bonding, with your reasoning. ((d)) The same plasma is probed by Raman scattering with a

532.0\,\mathrm{nm}

laser. At the AB vibrational shift of

840\,\mathrm{cm^{-1}}

(the same as

\Delta G''_{1/2}

found in part (a)), the Stokes line is

7.8

times more intense than the anti-Stokes line. Find the gas temperature.

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