- #1

BRN

- 108

- 10

1. Homework Statement

1. Homework Statement

Use the function of Lennard-Jones V (R) = ε [(σ / R)

^{12}- (σ / R)

^{6}] as model for the adiabatic potential energy in function of the separation between the

^{11}B boron and nitrogen nuclei

^{14}N. You determine the parameters ε and σ to reproduce the spectroscopic values of the vibrational quantum, ν = 1514.6 cm

^{-1}, and the separation of 1,666 cm

^{-1}between the lines of rotational BN molecule.

## The Attempt at a Solution

[/B]

I have

**ΔE**⇒

_{rot}=ħ^{2}/I=1.666 cm^{-1}=3.3091*10^{-23}J**I=**

**ħ**^{2}/**ΔE**

_{rot}=3.3603*10^{-46}Kgm^{2}and

R

R

_{0}=√(I/μ)=1.8125*10^{-10}mAt this point, I calculating the minimum oh the potential:

V(0)=∂

V(0)=∂

**V(R)**/∂R =0 ⇒ R_{0}^{6}=2σ^{6}⇒ σ=^{6}√(R_{0}^{6}/2)=1.6147*10^{-10}mFor ε, I calculating k by:

k=∂

k=∂

^{2}**V(R)**/∂R^{2}=6σ^{6}εR^{-14}(26σ^{6}-7R^{6})but here I'm lost...

Who can help me? Please!