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

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SUMMARY

The formula for calculating Kmin of a nucleon is expressed as K_{min} ≈ 3(hbar)π²/2ma², where a is approximately 2R_{0}A^{1/3} and R_{0} equals 1.07 fm. The derived expression for K_{min} results in a value of 133 MeV/A^{2/3}. The discussion highlights the importance of correctly applying the reduced Planck constant (hbar) and ensuring dimensional consistency in calculations. Participants emphasized the need for accurate unit conversions and the squaring of hbar in the formula.

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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
 
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Sorry but dimensions of your first formula are not correct.
 
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.
 

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