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(Solved): (17%%)H^(35)Cl is an example of a soft diatomic molecule whose natural vibration is 2886 cm^(-1). Us ...



(17%%)H^(35)Cl

is an example of a soft diatomic molecule whose natural vibration is 2886

cm^(-1)

. Using the harmonic oscillator model in problem 1 , determine the following quantities. (a) The value of the force constant

k_(h)

(b) Determine the value of the critical variation

(x_(t))

in the bond length of

H^(35)Cl

at the first excited state. (c) Express the tunneling probability of

H^(35)Cl

in its first excited state in terms of

\alpha

and

x_(t)

. Hint:

\int_0^t e^(-ax^(2))x^(2)dx=(1)/(4)((\pi )/(a^(3)))^((1)/(2))erf(\sqrt(a)t)-(te^(-at^(2)))/(2a)

and

\lim_(t->\infty )erf(t)->1
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