What is the formula for calculating Kmin of a nucleon and how can it be proven?

[Jason Gomez]

Homework Statement

Kmin of a nucleon is given by the expression

K_{min}\approx 3(hbar)\pi ^{2}/2ma^{2}

if a\approx 2R_{0}A^{1/3}

and R_{0}=1.07 fm

prove that K_{min}= 133Mev/A^{2/3}

Homework Equations

I used hbar=h/2\pi

The Attempt at a Solution

after plugging it all in I get
(3/4)h^{2}/(9.1596\times 10^{-30}m^{2}A^{2/3})
I know that h comes in units of Js and eVs, but then I still have seconds in the numerator and m in the denominator .
ps, only hints, I would like to solve on my own

 

[zzzoak]

Sorry but dimensions of your first formula are not correct.

 

[Jason Gomez]

yes, sorry about that. Looking it over I accidentally didn't square the hbar, but my intermediate result came from the correct formula. I am thinking there is another conversion factor that I am not thinking of, but I just can't figure it out.