4. Energetics of diatomic systems The energy of a diatomic molecule can be represented by the...
2.2) The Morse interatomic potential for a diatomic molecule is given by VM(r) D[1-e-a-1 r-ro where r is the interatomic distance. a) Sketch the potential, and indicate its attractive and repulsive region. [4 marks] b) Show that the equilibrium bond length is given by r ro. [4 marks] c) Determine the dissociation energy of the diatomic molecule. [4 marks]
The potential energy of two atoms in a diatomic molecule is approximated by U(r)=a/r^12−b/r^6, where r is the spacing between atoms and a and b are positive constants. Find the component of force along the line connecting the two atoms, Fr(r), on one atom as a function of r. Find the equilibrium distance between the two atoms. Is this equilibrium stable? Suppose the distance between the two atoms is equal to the equilibrium distance found in part A. What minimum...
The potential energy of two atoms in a diatomic molecule is approximated by U(r)=d/r12-b/r6, where r is the spacing between atoms and a and b are positive constants. Find the force F(r) on one atom as a function of r. Find the equilibrium distance between the two atoms. Express your answer in terms of the variables a and b. Is this equilibrium stable? Suppose the distance between the two atoms is equal to the equilibrium distance found in part (b)....
The potential energy of a diatomic molecule (a two-atom system like H, or 02) is given by А B E, (1) 76 where r is the separation of the two atoms of the molecule and A and B are positive constants. Eq. 1 is also known as Lennard-Jones potential. (a) Derive the force acting between the two atoms as a function of their distance r. [4 marks] (b) Find the system's equilibrium separation. [4 marks] (c) For a total mechanical...
Many diatomic (two-atom) molecules such as H2. 02, and N2 are bound together by covalent bonds. The interaction between two atoms can be described by a potential energy function of the following form, 2b Here, A, b, and ro are positive constants, and r is the center-to-center separation of the twa atoms. The mass of each atom is m CM Sketch U(r) versus r, and show that the two atoms are in stable equilibrium at r -ro- Find the total...
a) what effect does the change in internuclear separation in a diatomic molecule due to its vibration (the binding energy curve is asymmetric) have on the rotational energy levels of molecule? b)Explain why the separation between vibrational levels is somewhat smaller in an excited electronic state than in the ground electronic state. Explain the same effect for rotational states. c)show the ratio number of molecules in rotational level r to the number in the r=0 level, in a sample at...
3. Assuming atoms can be represented as hard spheres, the bonding energy between a sodium ion and a chloride ion pair can be represented by: 1.436 7.32x10-6 8 1 1 where U is energy per ion pair in eV and r is the separation distance between ions in nanometers. Write answers in units of eV and nm. a) Find the equation for force between the atom pair. b) Find the equilibrium separation distance ro- c) Estimate the elastic modulus for...
3. Assuming atoms can be represented as hard spheres, the bonding energy between a sodium ion and a chloride ion pair can be represented by: 1.436 7.32x10-6 8 1 1 where U is energy per ion pair in eV and r is the separation distance between ions in nanometers. Write answers in units of eV and nm. a) Find the equation for force between the atom pair. b) Find the equilibrium separation distance ro- c) Estimate the elastic modulus for...
Problem 2.18 The net potential energy between two adjacent ions, EN, may be represented by Where A, B, and n are constants whose values depend on the particular ionic system Calculate the bonding energy Eo in terms of the parameters A, B, and n using the following procedure: (1) Differentiate EN with respect to r, and then set the resulting expression equal to zero, since the curve of Ev versus r is a minimum at Eg. (2) Solve for r...
5. (10 points) A simple function that looks like the potential well of a diatomic molecule is the Morse potential given by: U(x) = D. (1-e-Bx) (1) where, x is the displacement of the bond from its equilibrium position, and D. is the value of U(x) at large separations. D. is called the classical dissociation energy and is characterized by the depth of the potential well. We can expand U(x) in a Taylor series about x = 0 to obtain...