# 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...
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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.)

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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