Problem with units? (trying to solve a normalized function)

[Labboi]

Homework Statement

I'm trying to solve a normalized function and cannot seem to get the right answer.

Relevant Equations

Kappa=sqrt(2m(EB)/hbar^2))
-kappa*R=-0.34

I'm trying to solve for this in a deuteron problem. But can't seem to get the right answer.
The reduced mass of the deuteron is 469.4 MeV, the binding energy Eb is 2.226 MeV and R = 1.5fm.

Using hbar = 6.5817x10^-16 eV.s

I get Kappa = sqrt((2(469.4)*2.226)/(6.5817*10^-22)^2) = 6.94*10^16

-kappa*(1.5*10^-13) = 10418.

I feel like I'm messing up units or something.

 

[Charles Link]

fm=1.0 E-15 m, but your arithmetic has other errors as well. Google of the mass of the deuteron also is in disagreement.

 

[vela]

I feel like I'm messing up units or something.

Like not including them on your answer? Have you tried including the units and working out the end result?

 

[vela]

fm=1.0 E-15 m

I disagree. One fm is $10^{-6}~\rm nm$.

 

[Charles Link]

When you put in for the mass, $m=E(in \, MeV)/c^2$.

 

[Steve4Physics]

I disagree. One fm is $10^{-6}~\rm nm$.

Then, in fact, you agree with @Charles Link!

 

[Labboi]

Kappa = Sqrt((2(469.4MeV/3.0*10^8m.s^-2)*2.226Mev)/(6.5817*10^-22MeV.s)^2 = 5939.86

-Kappa*R = 5939.86*1.5*10^-13 = 8.90*10^-13

I'm trying to convert the fm into cm

 

[Charles Link]

You need to take $c$ to the second power. In addition $\hbar$ is to the second power inside the square root. You need to do the arithmetic carefully.

 

[Labboi]

I did, just forgot it in the equation, sorry.

 

[Labboi]

Thank you, I must have messed up my parentheses, it's been a long night.