This problem is based on the concept of conversion of potential energy to force on atom and equilibrium distance between two atoms.
Initially, differentiate the potential energy expression to calculate the expression for the force with a negative sign, calculate the equilibrium distance between atoms.
Later, if potential energy is written in an expression, the differential of the potential energy with negative sign gives the force on the atom.
Finally, equilibrium distance is measured by using the expression of the force on the atom, this expression is equaled to zero to find the equilibrium distance.
The force is written as follows:
Here, is the function of potential energy.
The force should be zero, therefore it is written as follows:
Here, is the spacing between atoms, and are positive constants.
The case for stability is given as,
Here, is the function of force.
(a)
The expression for the potential energy of two atoms in a diatomic molecule is approximated as,
…… (1)
The force is written as,
…… (2)
From expression (1) and (2),
(b)
The equilibrium distance between two atoms is calculated as follows:
Further, it is written as follows:
Solve for r.
(c)
The case for stability is given as,
The differentiation of with respect to is written as follows:
Substitute the value for in above expression.
(d)
Substitute for and for in the equation .
(e)
The value of the aquarium distance for the Co molecule is equal to,
And the dissociation energy is as follows:
Therefore, from the equation and ,
Using the equation .
Solve for a.
(f)
Using the equation .
Substitute for a.
Ans: Part a
The force on one atom as a function of is .
Part bThe equilibrium distance between the two atoms is .
Part cThis Equilibrium is stable.
Part dThe dissociation energy is equal to .
Part eThe value of the constant a is equal to .
Part fThe value of the constant b is equal to .
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