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Problem 4. Consider the following reaction in which a species a approaches from -co and crosses

an energy barrier of height um at x = 0 and then falls in the potential well at b.

Let the left side (-∞0 < x≤ 0) of the potential be u(x)=um (1-2), where o is a small length

scale that called an activation length.

**

b

X

+00

In the class, we derived an equation for reaction flux as follows:

[Caeker

Сьека

J=D

Sekat dx

As you see, the forward flux is Jf = D_C₂BT

So ekB¹ dx

u(x)

Calculate this forward reaction flux using the expression for the potential u(x) given above.

Using a simple dimensional analysis, show what is the activation energy. What does the pre-

factor indicate? What would be the velocity of forward reaction?

Fig: 1