Fracture qustions The potential energy U of two atoms, a distance r apart, with a covalent bond is given by: m?

The potential energy U of two atoms, a distance r apart, with a covalent bond is given by: m n U A B r r =- + , m= 2 , n=10 (a) Indicate the physical significance of the two terms in the potential energy equation. (b) If the atoms form a stable molecule at a separation of 0.5 nm with an energy of -3 eV, calculate A... show more The potential energy U of two atoms, a distance r apart, with a covalent bond is given by:
m n
U A B
r r
=- + , m= 2 , n=10
(a) Indicate the physical significance of the two terms in the potential energy equation.
(b) If the atoms form a stable molecule at a separation of 0.5 nm with an energy of -3 eV,
calculate A and B. (1 nm=10-9 m, 1 eV =1.60´10-19 J )
(c) Calculate the force required to break the molecule, and the critical separation at
which the molecule breaks (dissociation radius and force).
(d) The bond stiffness, S, is given by:
2
2
S dF d U
dr dr
= =
and for small stretching, S is constant and equal to
0
2
0 2
r r
S d U
dr =
æç ÷ö=ççç ÷÷÷ è ø
This is the physical origin of Hooke’s Law, from which the elastic modulus can be
estimated by:
0
0
E S
r
=
Calculate E.
(e) Using a software, plot U (potential energy),
dU
dr
(force), and
2
2
d U
dr
(stiffness) as a
function of r. Identify characteristic values on these plots (Equilibrium distance,
dissociation distance, separation force etc.)
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