Physics for Scientists and Engineers
6th Edition
ISBN: 9781429281843
Author: Tipler
Publisher: MAC HIGHER
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Chapter 37, Problem 39P
To determine
The expression for equilibrium separation.
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One description of the potential energy of a diatomic molecule is given by the Lennard–Jones potential, U = (A)/(r12) - (B)/(r6)where A and B are constants and r is the separation distance between the atoms. Find, in terms of A and B, (a) the value r0 at which the energy is a minimum and (b) the energy E required to break up a diatomic molecule.
The potential energy of two atoms in a diatomic molecule is approximated by U(r) = a/r12-b/r6, where r is the spacing between atoms and a and b are positive constants.
Suppose the distance between the two atoms is equal to the equilibrium distance found in part A. What minimum energy must be added to the molecule to dissociate it -
that is, to separate the two atoms to an infinite distance apart? This is called the dissociation energy of the molecule. Express your answer in terms of the variables a and b.
For the molecule CO, the equilibrium distance between the carbon and oxygen atoms is 1.13\times 10-10m and the dissociation energy is 1.54\times 10-18J per
molecule. Find the value of the constant a. Express your answer in joules times meter in the twelth power. Find the value of the constant b. Express your answer in joules
times meter in the sixth power.
Consider two immiscible liquids such as water and oil. If a spherical oil molecule of radius r is taken out of the oil phase and placed in the water phase, the unfavorable energy of this transfer is proportional to the area of the solute (oil) molecule newly exposed to the solvent (water) multiplied by the interfacial energy, i, of the oil-water interface. The interfacial energy of the bulk cyclohexane-water interface is i = 50 mJ m-2, and the radius of a cyclohexane molecule is 0.28 nm. Using Boltzmann distribution, estimate the solubility of cyclohexane in water at 25 C in units of mol L-1.The concentration of water in water phase is 55.5 mol L-1.
Chapter 37 Solutions
Physics for Scientists and Engineers
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- Q/A particle of mass m moves in one dimension according to the potential energies . (a) V(æ)= a² + %3D (b) V(x) = kxe-bz (c) V (x) = k(xª – b²x²) %3D Find the equilibrium position for each state and test its stability?arrow_forward(a): Calculate Miller's indices in the hexagonal structure of its intersections. ai = 1, ar--1/2, as = 1,c= o and draw it. (b): the potential energy of a diatomic molecule is given by U = A B . where A and B are constants and r is the separation distance between the atoms. For the H2 molecule, take A = 0.124 x 10-120 eV. m2 and B = 1.488 x 10 eV.m. Find the separation distance at which the energy of the molecule is a minimum. Q3: Calculate the dhai of tetragonal using the concepts of reciprocal latticearrow_forwardQ3: The potential energy function for the force between two atoms in a diatomic molecule is approximately given by U(x) = - 읆 옮 , where a and b are constant and x is the distance between the atoms. If the dissociation energy of the molecule is (U(x= ∞) -U at equilibrium), D is (a) b²/6a (b) b²/2a (c) b²/12a (d) b²/4aarrow_forward
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