# Potential and wave number problem (concerning units)

1. Jun 18, 2013

### Lindsayyyy

Hi everyone I have the following problem:

1. The problem statement, all variables and given/known data

Give is the following potential for a molecule:

$$E_s(R)=E_s(\infty)-\frac {1}{R}+A*exp(-cR)$$

whereas E_s(infinity)=1.49 eV. A and c are constants which I want to calculate. R(equilibrium) is given as 2.36 Angström and the wave number for the lowest state is v=364,6 cm^-1

2. Relevant equations

3. The attempt at a solution

So far so good I already got the solution for this, but I have troubles concerning the units. If you take a look at the potential you have 1/R [m^-1] and E_s(infninity) whichs unit is [eV].

When I try to calculate c I derive the potential and use that the second derivation is the feather constant. I come to:

$$c=k*{R_0}^2 +\frac {2}{R_0}$$

whereas k is the feather constant and R0 the radius at the equilibrium.
The soluton for k should be: 0.0698 atomic units.

But I have no idea how to get there. I'm also conernced about the units because I only knew about N/m or kg/s^2 for k.

Can anyone help me with this?

2. Jun 18, 2013

### Simon Bridge

Not really enough information ... what are each of the constants supposed to represent physically?
i.e. if I take c=speed of light, then c=137 in Hartree atomic units.

http://en.wikipedia.org/wiki/Atomic_units

3. Jun 19, 2013

### Lindsayyyy

That information is not given. The task says that A and c are just constants whereas I shall find the values of each.

If I look at the potential c must have the unit m^-1 and A Joule

4. Jun 19, 2013

### Simon Bridge

Not if you are using atomic units.
Energy is given in Hartree energies and distance as a multiple of the Bohr radius.

You can't just read the units off like that:
If you look at the original expression, that 1/R must have dimensions of energy right?
If R has dimensions of length, then the "1" in 1/R must have dimensions of energy x length ...

... that's why you need to know where things come from.
Though, as long as the algebra is right, then putting atomic units in will get you atomic units out.
From what I see, c and k should be dimensionless.

5. Jun 20, 2013

### Lindsayyyy

Ok thank you,

I got the solution (the values of c and A) but I try to understand it. My first problem is that the solution says that the feather constants units are atomic units. How do I get there? (Value is written in my first post).

6. Jun 20, 2013

### Simon Bridge

I gave you a link to atomic units earlier - did you read it?