Question

La energía potencial entre dos átomos de una molécula diatómica puede ser modelada por el potencial de
Lennard–Jones,

- Uw=v( * )*-28) . . . 1..

, donde r es la distancia entre los átomos. Los parámetros
U0 y x0 se determinan experimentalmente.
a) Determine la fuerza F(r) que actúa sobre un átomo, como función de r. Haga dos gráficas, una de U(r)
contra r y una de F(r) contra r.
b) Encuentre la distancia de equilibrio entre los átomos en función de x0. ¿Es estable el equilibrio?
c) Llamemos r0 a la separación de equilibrio hallada en (b). Calcule U(r0) y a partir de esto, de una
interpretación al parámetro U0. ¿Cómo llamaría a este parámetro?
d) Para la molécula CO, la distancia de equilibrio entre los átomos de carbono y oxigeno es de 1,13× 10^-10 m y la energía de disociación es de 1,54×10^-18 J por molécula. Calcule el parámetro x0.

The potential energy between two atoms of a diatomic molecule can be modeled by the potential of Lennard-Jones,

, where r is the distance between the atoms. Parameters U0 and x0 are determined experimentally. a) Determine the force F (r) acting on an atom, as a function of r. Make two graphs, one of U (r) against r and one of F (r) against r. b) Find the equilibrium distance between the atoms as a function of x0. Is the balance stable? c) Let r0 be the equilibrium separation found in (b). Calculate U (r0) and from this, from a interpretation to parameter U0. What would you call this parameter? d) For the CO molecule, the equilibrium distance between carbon and oxygen atoms is 1.13 × 10^- 10 m and the dissociation energy is
1.54 × 10^-18 J per molecule. Calculate the parameter x0.

The potential energy between two atoms of a diatomic molecule can be modeled by the potential of Lennard-Jones, () 12 6 0 0 0 2 x x U r U r r       = -               , where r is the distance between the atoms. Parameters U0 and x0 are determined experimentally. a) Determine the force F (r) acting on an atom, as a function of r. Make two graphs, one of U (r) against r and one of F (r) against r. b) Find the equilibrium distance between the atoms as a function of x0. Is the balance stable? c) Let r0 be the equilibrium separation found in (b). Calculate U (r0) and from this, from a interpretation to parameter U0. What would you call this parameter? d) For the CO molecule, the equilibrium distance between carbon and oxygen atoms is 1.13 × 10- 10 m and the dissociation energy is 1.54 × 10-18 J per molecule. Calculate the parameter x0.

Answer 1

Me 12 || || ) | 1 = 2 |- || |

b) Equillibrum distance implies at Friso 13 po = no r=no onum distance is at r= no o c) To = x. =v Uz ve { ( 24 ) » _ 2 ( 2 ) Vw-) = Us (0) 2 (34= 0,01-0) -- Vero) = - U This point is called Equillibrium point podensial Yo Enugy is I minimum. Slable equillibrium point.